[was@modular verify_visible]$ [was@modular verify_visible]$ Magma V2.7-3      Tue Oct 31 2000 20:16:10 on modular  [Seed = 2673461278]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               ellap           idxG0
CS              MS              S               factormod       modcharpoly
DC              ND              Tn              factorpadic     padiccharpoly
ES              NS              Z               fcp             qexp
F               Q               charpoly        fn              x
> load "verify.m";
Loading "verify.m"
> a:=<1,<1,3>>;
> a:=$1;

>> a:=$1;
      ^
Runtime error: Previous value number (1) should be in the range [1 .. 0]
> a:=<1,<1,3>>;
> a;
<1, <1, 3>>
> a[1]
> ;
1
> a[2];
<1, 3>
> a:=[<1>, <2,3>];

>> a:=[<1>, <2,3>];
      ^
Runtime error in [ ... ]: Could not find a valid universe
>  a:=[* <1>, <2,3> *];
> a;
[* <1>, <2, 3> *]
> EllipticCurve;
Intrinsic 'EllipticCurve'

Signatures:

(<SeqEnum[RngElt]> S) -> CrvEll

The elliptic curve defined by the coefficients of S. S must be of length 2 or 5

(<RngElt> j) -> CrvEll

Creates an elliptic curve with j-invariant j

(<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> CrvEll

The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D

(<Rng> R, <RngElt> j) -> CrvEll

Returns an elliptic curve over R with j-invariant j

(<DB> D, <MonStgElt> S) -> SeqEnum

An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D.

(<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> SeqEnum

The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D.

(<CrvHyp> C) -> CrvEll, Map, Map

The elliptic curve E specified by the genus one hyperelliptic curve C of odd degree, followed by the morphism C -> E and its inverse.

(<CrvProjPl> C, <Pt> P) -> CrvEll, Map, Map

The elliptic curve E specified by the genus one curve C and the point P, followed by the birational map C -> E, and the morphism E -> C.

(<ModSym> M) -> SeqEnum
[
StartPrec,
Database
]

An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M.


> SetColumns(65);
> EllipticCurve;
Intrinsic 'EllipticCurve'

Signatures:

    (<SeqEnum[RngElt]> S) -> CrvEll

        The elliptic curve defined by the coefficients of S. S 
        must be of length 2 or 5

    (<RngElt> j) -> CrvEll

        Creates an elliptic curve with j-invariant j

    (<DB> D, <RngIntElt> N, <RngIntElt> I, <RngIntElt> J) -> 
    CrvEll

        The J-th elliptic curve in the I-th isogeny class of 
        conductor N found in the elliptic curve database D

    (<Rng> R, <RngElt> j) -> CrvEll

        Returns an elliptic curve over R with j-invariant j

    (<DB> D, <MonStgElt> S) -> SeqEnum

        An elliptic curve with label S (e.g. "101A" or "101A1") 
        in the elliptic curve database D.

    (<DB> D, <RngIntElt> N, <MonStgElt> S, <RngIntElt> J) -> 
    SeqEnum

        The J-th elliptic curve of conductor N and label S (e.g. 
        "A") in the elliptic curve database D.

    (<CrvHyp> C) -> CrvEll, Map, Map

        The elliptic curve E specified by the genus one 
        hyperelliptic curve C of odd degree, followed by the 
        morphism C -> E and its inverse.

    (<CrvProjPl> C, <Pt> P) -> CrvEll, Map, Map

        The elliptic curve E specified by the genus one curve C 
        and the point P, followed by the birational map C -> E, 
        and the morphism E -> C.

    (<ModSym> M) -> SeqEnum
    [
        StartPrec,
        Database
    ]

        An elliptic curve over the rational numbers that lies in 
        the isogeny class of elliptic curves associated to M.


> load "verify.m";
Loading "verify.m"
> E(visdat[1][2]);
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 1154*x - 15345 
over Rational Field
> load "verify.m";
Loading "verify.m"
> E(visdat[1][2]);
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 1154*x - 15345 
over Rational Field
> E(no_curve)
> ;

E(
    label: [ 0, 0 ]
)
In file "verify.m", line 60, column 24:
>>    assert label ne no_curve;
                          ^
Runtime error in 'EllipticCurve': Conductor must be positive
> E(no_curve)
> ;

E(
    label: [ 0, 0 ]
)
In file "verify.m", line 60, column 24:
>>    if label eq no_curve then
                          ^
Runtime error in 'EllipticCurve': Conductor must be positive
> load "verify.m";
Loading "verify.m"
> E(no_curve)
> ;
No such curve.
> load "verify.m";
Loading "verify.m"
> verify_ranks()
> ;
Lie in  <3, [ 681, 2 ], [ 681, 3 ]>
: rank is not two.
> e:=E([681,3]);
> e;
Elliptic Curve defined by y^2 + y = x^3 - x^2 + 2 over Rational 
Field
> Rank(e);
2
> load "verify.m";
Loading "verify.m"
> verify_ranks()
> ;
<3, [ 681, 2 ], [ 681, 3 ]>
passed.

[Interrupt twice in half a second; exiting]

Total time: 8.489 seconds
[was@modular verify_visible]$ 
[was@modular verify_visible]$ exit
exit

Process magma exited abnormally with code 1

[was@modular verify_visible]$ [was@modular verify_visible]$ Magma V2.7-3      Tue Oct 31 2000 20:52:39 on modular  [Seed = 417224229]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               ellap           idxG0
CS              MS              S               factormod       modcharpoly
DC              ND              Tn              factorpadic     padiccharpoly
ES              NS              Z               fcp             qexp
F               Q               charpoly        fn              x
> Rank;
Intrinsic 'Rank'

Signatures:

(<AlgMatElt> X) -> RngIntElt
(<ModMatRngElt> X) -> RngIntElt

The rank of X

(<ModTupRng> M) -> RngIntElt
(<ModMatRng> M) -> RngIntElt
(<ModRng> M) -> RngIntElt
(<ModED> M) -> RngIntElt

The rank of the free module M over its base coefficient ring

(<RngUPol> R) -> RngIntElt
(<RngMPol> R) -> RngIntElt
(<RngMPolRes> R) -> RngIntElt
(<FldFunRat> R) -> RngIntElt

The number of indeterminates of R over its coefficient ring

(<FldAC> A) -> RngIntElt

The current number of indeterminates of A

(<Lat> L) -> RngIntElt

The rank of the lattice L

(<CrvEll> E) -> RngIntElt
[
Bound: RngIntElt
]

The (lower bound on the) rank of the Mordell-Weil group of E; E must be defined over Q

(<IncGeom> D) -> RngIntElt

The rank of the incidence geometry D

(<CosetGeom> D) -> RngIntElt

The rank of the coset geometry D

(<SymGen> G) -> RngIntElt

The rank of the genus.

(<SymGenLoc> G) -> RngIntElt

The rank of the genus.


> load "verify.m";
Loading "verify.m"
> e:=E(visdata[2][2]);f:=E(visdata[2][3]);

>> e:=E(visdata[2][2]);f:=E(visdata[2][3]);
        ^
User error: Identifier 'visdata' has not been declared or assigned

>> e:=E(visdata[2][2]);f:=E(visdata[2][3]);
                            ^
User error: Identifier 'visdata' has not been declared or assigned
> load "verify.m";
Loading "verify.m"
>  e:=E(visdat[2][2]);f:=E(visdat[2][3]);
> RankBounds(e);

[Interrupt twice in half a second; exiting]

Total time: 33.860 seconds
[was@modular verify_visible]$ exit
exit

Process magma finished
[was@modular verify_visible]$ [was@modular verify_visible]$ Magma V2.7-3      Tue Oct 31 2000 20:55:51 on modular  [Seed = 973043780]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               ellap           idxG0
CS              MS              S               factormod       modcharpoly
DC              ND              Tn              factorpadic     padiccharpoly
ES              NS              Z               fcp             qexp
F               Q               charpoly        fn              x
> load "verify.m";
Loading "verify.m"
> e:=E(visdat[2][2]);f:=E(visdat[2][3]);
> RankBounds(f);
2 2
> Rank(f);
2
> load "verify.m";
Loading "verify.m"
> verify_ranks();
<3, [ 681, 2 ], [ 681, 3 ]>
passed.
<5, [ 1058, 4 ], [ 1058, 3 ]>
passed.
<5, [ 1246, 2 ], [ 1246, 3 ]>
passed.
<5, [ 1664, 11 ], [ 1664, 14 ]>
passed.
<3, [ 1913, 2 ], [ 1913, 1 ]>
passed.
<3, [ 2006, 5 ], [ 2006, 4 ]>
passed.
<3, [ 2366, 4 ], [ 2366, 5 ]>
passed.
<5, [ 2366, 6 ], [ 2366, 5 ]>
passed.
<3, [ 2429, 2 ], [ 2429, 4 ]>
passed.
<3, [ 2534, 5 ], [ 2534, 7 ]>
passed.
<3, [ 2534, 6 ], [ 2534, 7 ]>
passed.
<3, [ 2541, 4 ], [ 2541, 3 ]>
passed.
<5, [ 2574, 4 ], [ 2574, 7 ]>
passed.
<3, [ 2601, 8 ], [ 2601, 12 ]>
passed.
<3, [ 2674, 2 ], [ 2674, 1 ]>
passed.
<3, [ 2710, 3 ], [ 2710, 2 ]>
passed.
<3, [ 2718, 4 ], [ 2710, 2 ]>
passed.
<3, [ 2768, 3 ], [ 2768, 2 ]>
passed.
<5, [ 2834, 4 ], [ 2834, 3 ]>
passed.
<5, [ 2900, 4 ], [ 2900, 3 ]>
passed.
<3, [ 2955, 2 ], [ 2955, 3 ]>
passed.
<3, [ 3054, 1 ], [ 3054, 3 ]>
passed.
<5, [ 3185, 3 ], [ 3185, 2 ]>
passed.
<3, [ 3306, 2 ], [ 1102, 1 ]>
passed.
<5, [ 3384, 1 ], [ 3384, 3 ]>
passed.
<3, [ 3536, 8 ], [ 3536, 7 ]>
passed.
<3, [ 3555, 5 ], [ 3555, 4 ]>
passed.
<3, [ 3712, 10 ], [ 3712, 9 ]>
passed.
<3, [ 3879, 5 ], [ 3879, 4 ]>
passed.
<3, [ 3933, 1 ], [ 3933, 2 ]>
passed.
<5, [ 3952, 3 ], [ 3952, 5 ]>
passed.
<3, [ 3954, 3 ], [ 3954, 4 ]>
passed.
<5, [ 4092, 1 ], [ 4092, 2 ]>
passed.
<5, [ 4592, 4 ], [ 4592, 7 ]>
passed.
<3, [ 4592, 6 ], [ 4592, 3 ]>
passed.
<3, [ 4592, 6 ], [ 4592, 7 ]>
passed.
<3, [ 4606, 2 ], [ 4606, 3 ]>
passed.
<3, [ 4675, 10 ], [ 4675, 9 ]>
passed.
<3, [ 4963, 3 ], [ 4963, 4 ]>
passed.
<3, [ 5046, 8 ], [ 5046, 10 ]>
passed.
<5, [ 5082, 3 ], [ 5082, 4 ]>
passed.
<3, [ 5136, 2 ], [ 1712, 4 ]>
passed.

verify_ranks(
)
E(
label: [ 5499, 5 ]
)
In file "verify.m", line 63, column 24:
>>    return EllipticCurve(CremonaDatabase(),label[1],label[2],1);
                          ^
Runtime error in 'EllipticCurve': Conductor 5499 is not stored in database
> load "verify.m";
Loading "verify.m"
> e=E(visdat[3][2]);
Elliptic Curve defined by y^2 + x*y = x^3 - x^2 - 332311*x - 73733731 over Rational Field = Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 10688904*x - 13455247360 over Rational Field
> Rank(e);

[Interrupt twice in half a second; exiting]

Total time: 42.919 seconds
[was@modular verify_visible]$ exit
exit

Process magma finished
[was@modular verify_visible]$ [was@modular verify_visible]$ Magma V2.7-3      Tue Oct 31 2000 20:57:35 on modular  [Seed = 921728995]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               ellap           idxG0
CS              MS              S               factormod       modcharpoly
DC              ND              Tn              factorpadic     padiccharpoly
ES              NS              Z               fcp             qexp
F               Q               charpoly        fn              x
> Type(EllipticCurve([1,2,3,4,5]));
CrvEll
> load "verify.m";
Loading "verify.m"
> verify_visible();

verify_visible(
)
E(
label: 681
)
In file "verify.m", line 64, column 13:
>>    if label eq no_curve then
               ^
Runtime error in 'eq': Bad argument types
Argument types given: RngIntElt, SeqEnum[RngIntElt]
> visdat;
[
<3, [ 681, 2 ], [ 681, 3 ]>,
<5, [ 1058, 4 ], [ 1058, 3 ]>,
<5, [ 1246, 2 ], [ 1246, 3 ]>,
<5, [ 1664, 11 ], [ 1664, 14 ]>,
<3, [ 1913, 2 ], [ 1913, 1 ]>,
<3, [ 2006, 5 ], [ 2006, 4 ]>,
<3, [ 2366, 4 ], [ 2366, 5 ]>,
<5, [ 2366, 6 ], [ 2366, 5 ]>,
<3, [ 2429, 2 ], [ 2429, 4 ]>,
<3, [ 2534, 5 ], [ 2534, 7 ]>,
<3, [ 2534, 6 ], [ 2534, 7 ]>,
<3, [ 2541, 4 ], [ 2541, 3 ]>,
<5, [ 2574, 4 ], [ 2574, 7 ]>,
<3, [ 2601, 8 ], [ 2601, 12 ]>,
<3, [ 2674, 2 ], [ 2674, 1 ]>,
<3, [ 2710, 3 ], [ 2710, 2 ]>,
<3, [ 2718, 4 ], [ 2710, 2 ]>,
<3, [ 2768, 3 ], [ 2768, 2 ]>,
<5, [ 2834, 4 ], [ 2834, 3 ]>,
<3, [ 2849, 1 ], [ 0, 0 ]>,
<5, [ 2900, 4 ], [ 2900, 3 ]>,
<3, [ 2932, 1 ], [ 0, 0 ]>,
<3, [ 2955, 2 ], [ 2955, 3 ]>,
<3, [ 3054, 1 ], [ 3054, 3 ]>,
<5, [ 3185, 3 ], [ 3185, 2 ]>,
<3, [ 3306, 2 ], [ 1102, 1 ]>,
<7, [ 3364, 3 ], [ 0, 0 ]>,
<5, [ 3384, 1 ], [ 3384, 3 ]>,
<3, [ 3536, 8 ], [ 3536, 7 ]>,
<3, [ 3555, 5 ], [ 3555, 4 ]>,
<3, [ 3712, 10 ], [ 3712, 9 ]>,
<3, [ 3879, 5 ], [ 3879, 4 ]>,
<3, [ 3933, 1 ], [ 3933, 2 ]>,
<5, [ 3952, 3 ], [ 3952, 5 ]>,
<3, [ 3954, 3 ], [ 3954, 4 ]>,
<5, [ 4092, 1 ], [ 4092, 2 ]>,
<3, [ 4229, 1 ], [ 0, 0 ]>,
<3, [ 4343, 3 ], [ 0, 0 ]>,
<5, [ 4592, 4 ], [ 4592, 7 ]>,
<3, [ 4592, 6 ], [ 4592, 3 ]>,
<3, [ 4592, 6 ], [ 4592, 7 ]>,
<3, [ 4606, 2 ], [ 4606, 3 ]>,
<3, [ 4675, 10 ], [ 4675, 9 ]>,
<3, [ 4914, 14 ], [ 0, 0 ]>,
<3, [ 4963, 3 ], [ 4963, 4 ]>,
<3, [ 5046, 8 ], [ 5046, 10 ]>,
<3, [ 5054, 3 ], [ 0, 0 ]>,
<3, [ 5073, 4 ], [ 0, 0 ]>,
<5, [ 5082, 3 ], [ 5082, 4 ]>,
<3, [ 5136, 2 ], [ 1712, 4 ]>,
<3, [ 5389, 1 ], [ 0, 0 ]>
]
> load "verify.m";
Loading "verify.m"
> verify_visible();
[ 681, 3 ]

verify_visible(
)
E(
label: 681
)
In file "verify.m", line 64, column 13:
>>    if label eq no_curve then
               ^
Runtime error in 'eq': Bad argument types
Argument types given: RngIntElt, SeqEnum[RngIntElt]
> load "verify.m";verify_visible();
Loading "verify.m"
> 
[ 681, 3 ]
At level 681  p divides the level.

verify_visible(
)
In file "verify.m", line 126, column 26:
>>          if Product_cpbar(e) mod p eq 0 then
                            ^
Runtime error: No return statement executed in user-defined function
> load "verify.m";
Loading "verify.m"
> verify_visible();
[ 681, 3 ]
At level 681  p divides the level.

verify_visible(
)
Product_cpbar(
e: e
)
In file "verify.m", line 106, column 48:
>>    return &*[cpbar(e,p[1]) : p in Factorization(Discriminant(e))];
                                                  ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldRatElt
> verify_visible();
[ 681, 3 ]
At level 681  p divides the level.

verify_visible(
)
Product_cpbar(
e: e
)
In file "verify.m", line 106, column 48:
>>    return &*[cpbar(e,p[1]) : p in Factorization(Conductor(e))];
                                                  ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldRatElt
> load "verify.m";verify_visible();
Loading "verify.m"
[ 681, 3 ]
At level 681  p divides the level.
[ 1058, 3 ]
[ 1246, 3 ]
[ 1664, 14 ]
[ 1913, 1 ]
[ 2006, 4 ]
[ 2366, 5 ]
At level 2366  p divides the prod cpbar(E).
At level 2366  p divides the prod cp(F).
[ 2366, 5 ]
[ 2429, 4 ]
[ 2534, 7 ]
[ 2534, 7 ]
[ 2541, 3 ]
At level 2541  p divides the level.
[ 2574, 7 ]
[ 2601, 12 ]
At level 2601  p divides the level.
[ 2674, 1 ]
[ 2710, 2 ]
At level 2710  p divides the prod cpbar(E).
[ 2710, 2 ]
At level 2718  p divides the level.
[ 2768, 2 ]
[ 2834, 3 ]
[ 0, 0 ]
[ 2900, 3 ]
At level 2900  p divides the level.
[ 0, 0 ]
[ 2955, 3 ]
At level 2955  p divides the level.
At level 2955  p divides the prod cpbar(E).
At level 2955  p divides the prod cp(F).
[ 3054, 3 ]
At level 3054  p divides the level.
[ 3185, 2 ]
At level 3185  p divides the level.
[ 1102, 1 ]
At level 3306  p divides the level.
At level 3306  p divides the prod cpbar(E).
[ 0, 0 ]
[ 3384, 3 ]
[ 3536, 7 ]
[ 3555, 4 ]
At level 3555  p divides the level.
[ 3712, 9 ]
[ 3879, 4 ]
At level 3879  p divides the level.
[ 3933, 2 ]
At level 3933  p divides the level.
[ 3952, 5 ]
[ 3954, 4 ]
At level 3954  p divides the level.
[ 4092, 2 ]
[ 0, 0 ]
[ 0, 0 ]
[ 4592, 7 ]
[ 4592, 3 ]
[ 4592, 7 ]
[ 4606, 3 ]
At level 4606  p divides the prod cpbar(E).
[ 4675, 9 ]
At level 4675  p divides the prod cpbar(E).
At level 4675  p divides the prod cp(F).
[ 0, 0 ]
[ 4963, 4 ]
[ 5046, 10 ]
At level 5046  p divides the level.
[ 0, 0 ]
[ 0, 0 ]
[ 5082, 4 ]
[ 1712, 4 ]
At level 5136  p divides the level.
At level 5136  p divides the prod cpbar(E).
[ 0, 0 ]

>> load "verify.m";verify_visible();
                                 ^
Runtime error in procedure call: No return statement executed in user-defined function
> load "verify.m";verify_visible();
Loading "verify.m"
At level 681  p divides the level.
At level 2366  p divides the prod cpbar(E).
At level 2366  p divides the prod cp(F).
At level 2541  p divides the level.
At level 2601  p divides the level.
At level 2710  p divides the prod cpbar(E).
At level 2718  p divides the level.
At level 2900  p divides the level.
At level 2955  p divides the level.
At level 2955  p divides the prod cpbar(E).
At level 2955  p divides the prod cp(F).
At level 3054  p divides the level.
At level 3185  p divides the level.
At level 3306  p divides the level.
At level 3306  p divides the prod cpbar(E).
At level 3555  p divides the level.
At level 3879  p divides the level.
At level 3933  p divides the level.
At level 3954  p divides the level.
At level 4606  p divides the prod cpbar(E).
At level 4675  p divides the prod cpbar(E).
At level 4675  p divides the prod cp(F).
At level 5046  p divides the level.
At level 5136  p divides the level.
At level 5136  p divides the prod cpbar(E).
> 681 mod 3;
0
> load "verify.m";verify_visible();
Loading "verify.m"
At level 681  p = 3  divides the level.
At level 2366  p = 3  divides the prod cpbar(E).
At level 2366  p = 3  divides the prod cp(F).
At level 2541  p = 3  divides the level.
At level 2601  p = 3  divides the level.
At level 2710  p = 3  divides the prod cpbar(E).
At level 2718  p = 3  divides the level.
At level 2900  p = 5  divides the level.
At level 2955  p = 3  divides the level.
At level 2955  p = 3  divides the prod cpbar(E).
At level 2955  p = 3  divides the prod cp(F).
At level 3054  p = 3  divides the level.
At level 3185  p = 5  divides the level.
At level 3306  p = 3  divides the level.
At level 3306  p = 3  divides the prod cpbar(E).
At level 3555  p = 3  divides the level.
At level 3879  p = 3  divides the level.
At level 3933  p = 3  divides the level.
At level 3954  p = 3  divides the level.
At level 4606  p = 3  divides the prod cpbar(E).
At level 4675  p = 3  divides the prod cpbar(E).
At level 4675  p = 3  divides the prod cp(F).
At level 5046  p = 3  divides the level.
At level 5136  p = 3  divides the level.
At level 5136  p = 3  divides the prod cpbar(E).
> load "verify.m";verify_visible();
Loading "verify.m"
At level 681  p = 3  divides the level.
OK at level 1058
OK at level 1246
OK at level 1664
OK at level 1913
OK at level 2006
At level 2366  p = 3  divides the prod cpbar(E).
At level 2366  p = 3  divides the prod cp(F).
OK at level 2366
OK at level 2429
OK at level 2534
OK at level 2534
At level 2541  p = 3  divides the level.
OK at level 2574
At level 2601  p = 3  divides the level.
OK at level 2674
At level 2710  p = 3  divides the prod cpbar(E).
At level 2718  p = 3  divides the level.
OK at level 2768
OK at level 2834
At level 2900  p = 5  divides the level.
At level 2955  p = 3  divides the level.
At level 2955  p = 3  divides the prod cpbar(E).
At level 2955  p = 3  divides the prod cp(F).
At level 3054  p = 3  divides the level.
At level 3185  p = 5  divides the level.
At level 3306  p = 3  divides the level.
At level 3306  p = 3  divides the prod cpbar(E).
OK at level 3384
OK at level 3536
At level 3555  p = 3  divides the level.
OK at level 3712
At level 3879  p = 3  divides the level.
At level 3933  p = 3  divides the level.
OK at level 3952
At level 3954  p = 3  divides the level.
OK at level 4092
OK at level 4592
OK at level 4592
OK at level 4592
At level 4606  p = 3  divides the prod cpbar(E).
At level 4675  p = 3  divides the prod cpbar(E).
At level 4675  p = 3  divides the prod cp(F).
OK at level 4963
At level 5046  p = 3  divides the level.
OK at level 5082
At level 5136  p = 3  divides the level.
At level 5136  p = 3  divides the prod cpbar(E).
> load "verify.m";verify_visible();
Loading "verify.m"




681 :  p = 3  divides the level.
1058 : OK
1246 : OK
1664 : OK
1913 : OK
2006 : OK
2366 :  p = 3  divides the prod cpbar(E).
2366 :  p = 3  divides the prod cp(F).
2366 : OK
2429 : OK
2534 : OK
2534 : OK
2541 :  p = 3  divides the level.
2574 : OK
2601 :  p = 3  divides the level.
2674 : OK
2710 :  p = 3  divides the prod cpbar(E).
2718 :  p = 3  divides the level.
2768 : OK
2834 : OK
2900 :  p = 5  divides the level.
2955 :  p = 3  divides the level.
2955 :  p = 3  divides the prod cpbar(E).
2955 :  p = 3  divides the prod cp(F).
3054 :  p = 3  divides the level.
3185 :  p = 5  divides the level.
3306 :  p = 3  divides the level.
3306 :  p = 3  divides the prod cpbar(E).
3384 : OK
3536 : OK
3555 :  p = 3  divides the level.
3712 : OK
3879 :  p = 3  divides the level.
3933 :  p = 3  divides the level.
3952 : OK
3954 :  p = 3  divides the level.
4092 : OK
4592 : OK
4592 : OK
4592 : OK
4606 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cp(F).
4963 : OK
5046 :  p = 3  divides the level.
5082 : OK
5136 :  p = 3  divides the level.
5136 :  p = 3  divides the prod cpbar(E).
> load "verify.m";verify_visible();
Loading "verify.m"
681  :  p = 3  divides the level.
1058 :  OK
1246 :  OK
1664 :  OK
1913 :  OK
2006 :  OK
2366 :  p = 3  divides the prod cpbar(E).
2366 :  p = 3  divides the prod cp(F).
2366 :  OK
2429 :  OK
2534 :  OK
2534 :  OK
2541 :  p = 3  divides the level.
2574 :  OK
2601 :  p = 3  divides the level.
2674 :  OK
2710 :  p = 3  divides the prod cpbar(E).
2718 :  p = 3  divides the level.
2768 :  OK
2834 :  OK
2900 :  p = 5  divides the level.
2955 :  p = 3  divides the level.
2955 :  p = 3  divides the prod cpbar(E).
2955 :  p = 3  divides the prod cp(F).
3054 :  p = 3  divides the level.
3185 :  p = 5  divides the level.
3306 :  p = 3  divides the level.
3306 :  p = 3  divides the prod cpbar(E).
3384 :  OK
3536 :  OK
3555 :  p = 3  divides the level.
3712 :  OK
3879 :  p = 3  divides the level.
3933 :  p = 3  divides the level.
3952 :  OK
3954 :  p = 3  divides the level.
4092 :  OK
4592 :  OK
4592 :  OK
4592 :  OK
4606 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cp(F).
4963 :  OK
5046 :  p = 3  divides the level.
5082 :  OK
5136 :  p = 3  divides the level.
5136 :  p = 3  divides the prod cpbar(E).
> load "verify.m";verify_visible();
Loading "verify.m"
681 :  p = 3  divides the level.
Additive reduction for N= 1058
1058 :  OK
1246 :  OK
Additive reduction for N= 1664
1664 :  OK
1913 :  OK
2006 :  OK
Additive reduction for N= 2366
2366 :  p = 3  divides the prod cpbar(E).
2366 :  p = 3  divides the prod cp(F).
Additive reduction for N= 2366
2366 :  OK
2429 :  OK
2534 :  OK
2534 :  OK
2541 :  p = 3  divides the level.
Additive reduction for N= 2541
Additive reduction for N= 2574
2574 :  OK
2601 :  p = 3  divides the level.
Additive reduction for N= 2601
Additive reduction for N= 2601
2674 :  OK
2710 :  p = 3  divides the prod cpbar(E).
2718 :  p = 3  divides the level.
Additive reduction for N= 2718
Additive reduction for N= 2768
2768 :  OK
2834 :  OK
2900 :  p = 5  divides the level.
Additive reduction for N= 2900
Additive reduction for N= 2900
2955 :  p = 3  divides the level.
2955 :  p = 3  divides the prod cpbar(E).
2955 :  p = 3  divides the prod cp(F).
3054 :  p = 3  divides the level.
3185 :  p = 5  divides the level.
Additive reduction for N= 3185
3306 :  p = 3  divides the level.
3306 :  p = 3  divides the prod cpbar(E).
Additive reduction for N= 3384
Additive reduction for N= 3384
3384 :  OK
Additive reduction for N= 3536
3536 :  OK
3555 :  p = 3  divides the level.
Additive reduction for N= 3555
Additive reduction for N= 3712
3712 :  OK
3879 :  p = 3  divides the level.
Additive reduction for N= 3879
3933 :  p = 3  divides the level.
Additive reduction for N= 3933
Additive reduction for N= 3952
3952 :  OK
3954 :  p = 3  divides the level.
Additive reduction for N= 4092
4092 :  OK
Additive reduction for N= 4592
4592 :  OK
Additive reduction for N= 4592
4592 :  OK
Additive reduction for N= 4592
4592 :  OK
Additive reduction for N= 4606
4606 :  p = 3  divides the prod cpbar(E).
Additive reduction for N= 4675
4675 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cp(F).
4963 :  OK
5046 :  p = 3  divides the level.
Additive reduction for N= 5046
Additive reduction for N= 5082
5082 :  OK
5136 :  p = 3  divides the level.
Additive reduction for N= 5136
5136 :  p = 3  divides the prod cpbar(E).
> SquareFree;
Intrinsic 'SquareFree'

Signatures:

(<RngIntElt> a) -> RngIntElt, RngIntElt
(<RngIntEltFact> a) -> RngIntEltFact, RngIntEltFact

Return a squarefree integer x as well as an integer y, such that a = x*y^2


> IsSquareFree;

>> IsSquareFree;
   ^
User error: Identifier 'IsSquareFree' has not been declared or assigned
> load "verify.m";verify_visible();
Loading "verify.m"
681 :  p = 3  divides the level.
1058 :  additive reduction.
1246 :  OK
1664 :  additive reduction.
1913 :  OK
2006 :  OK
2366 :  p = 3  divides the prod cpbar(E).
2366 :  p = 3  divides the prod cp(F).
2366 :  additive reduction.
2366 :  additive reduction.
2429 :  OK
2534 :  OK
2534 :  OK
2541 :  p = 3  divides the level.
2541 :  additive reduction.
2574 :  additive reduction.
2601 :  p = 3  divides the level.
2601 :  additive reduction.
2674 :  OK
2710 :  p = 3  divides the prod cpbar(E).
2718 :  p = 3  divides the level.
2718 :  additive reduction.
2768 :  additive reduction.
2834 :  OK
2900 :  p = 5  divides the level.
2900 :  additive reduction.
2955 :  p = 3  divides the level.
2955 :  p = 3  divides the prod cpbar(E).
2955 :  p = 3  divides the prod cp(F).
3054 :  p = 3  divides the level.
3185 :  p = 5  divides the level.
3185 :  additive reduction.
3306 :  p = 3  divides the level.
3306 :  p = 3  divides the prod cpbar(E).
3384 :  additive reduction.
3536 :  additive reduction.
3555 :  p = 3  divides the level.
3555 :  additive reduction.
3712 :  additive reduction.
3879 :  p = 3  divides the level.
3879 :  additive reduction.
3933 :  p = 3  divides the level.
3933 :  additive reduction.
3952 :  additive reduction.
3954 :  p = 3  divides the level.
4092 :  additive reduction.
4592 :  additive reduction.
4592 :  additive reduction.
4592 :  additive reduction.
4606 :  p = 3  divides the prod cpbar(E).
4606 :  additive reduction.
4675 :  p = 3  divides the prod cpbar(E).
4675 :  p = 3  divides the prod cp(F).
4675 :  additive reduction.
4963 :  OK
5046 :  p = 3  divides the level.
5046 :  additive reduction.
5082 :  additive reduction.
5136 :  p = 3  divides the level.
5136 :  p = 3  divides the prod cpbar(E).
5136 :  additive reduction.
>