[was@modular hsia]$ [was@modular hsia]$ Magma V2.8-2      Thu Jan 17 2002 15:50:10 on modular  [Seed = 2748884651]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> E := EllipticCurve(CremonaDatabase(),"37A");
>  G,f := MordellWeilGroup(E);
> P := f(G.1);
> P;
(0 : 0 : 1)
> EE := ChangeRing(E,GF(2003));
> Order(EE!P);
664
> P := [p : p in [2..3000] | IsPrime(p)];
> #P;
430
> P := [p : p in [2..3000] | IsPrime(p) and Conductor(E) mod p ne 0];
> Q := f(G.1);
> Q;
(0 : 0 : 1)
> time ords := [Order(ChangeRing(E,GF(p))!Q) : p in P];
Time: 4.550
> ords := Sort(ords);
> ords;
[ 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 17, 18, 18, 20, 20, 25, 27, 28, 30, 31, 33, 33, 33, 35, 35, 36, 38, 39, 41, 44, 45, 47, 47, 49, 49, 50, 51, 53, 53, 54, 55, 57, 59, 61, 63, 63, 64, 68, 72, 73, 74, 74, 75, 75, 76, 81, 86, 86, 87, 89, 91, 92, 93, 96, 99, 103, 103, 103, 104, 106, 110, 113, 114, 116, 119, 121, 122, 123, 126, 127, 127, 128, 129, 132, 132, 133, 134, 135, 135, 137, 138, 138, 144, 144, 148, 150, 152, 154, 154, 155, 155, 156, 167, 172, 172, 177, 178, 178, 179, 180, 180, 182, 188, 188, 191, 193, 195, 199, 202, 202, 207, 207, 209, 217, 220, 220, 223, 227, 227, 228, 233, 241, 243, 248, 250, 254, 255, 259, 260, 261, 270, 272, 273, 284, 292, 297, 297, 302, 303, 305, 315, 317, 325, 339, 344, 346, 346, 356, 360, 370, 370, 373, 375, 376, 384, 393, 398, 403, 403, 404, 410, 412, 413, 414, 414, 417, 417, 421, 425, 428, 432, 440, 443, 444, 446, 448, 457, 469, 475, 476, 484, 486, 488, 490, 491, 507, 512, 518, 520, 520, 525, 527, 528, 531, 538, 538, 541, 544, 545, 546, 546, 555, 555, 556, 562, 565, 565, 566, 568, 578, 594, 597, 599, 599, 599, 601, 620, 626, 638, 639, 640, 643, 646, 647, 650, 653, 655, 656, 656, 660, 664, 665, 669, 678, 685, 688, 689, 690, 691, 699, 712, 723, 727, 727, 738, 749, 766, 774, 783, 793, 797, 808, 813, 814, 814, 818, 836, 845, 863, 869, 872, 874, 878, 880, 881, 886, 889, 893, 896, 896, 919, 933, 936, 955, 974, 978, 978, 979, 981, 986, 1031, 1052, 1057, 1057, 1058, 1084, 1099, 1100, 1102, 1125, 1136, 1145, 1158, 1160, 1166, 1177, 1185, 1205, 1211, 1221, 1226, 1242, 1242, 1257, 1259, 1263, 1272, 1278, 1287, 1296, 1298, 1319, 1322, 1324, 1330, 1336, 1339, 1357, 1411, 1412, 1425, 1430, 1454, 1459, 1463, 1469, 1473, 1491, 1493, 1497, 1505, 1508, 1516, 1523, 1542, 1549, 1564, 1566, 1570, 1585, 1605, 1668, 1674, 1713, 1720, 1729, 1738, 1762, 1781, 1799, 1806, 1824, 1833, 1889, 1921, 1923, 1931, 1961, 1966, 1981, 2029, 2053, 2054, 2075, 2092, 2093, 2098, 2135, 2153, 2155, 2157, 2162, 2172, 2193, 2197, 2200, 2202, 2244, 2270, 2281, 2283, 2287, 2311, 2316, 2333, 2341, 2352, 2359, 2371, 2384, 2407, 2409, 2450, 2460, 2470, 2492, 2521, 2553, 2554, 2569, 2570, 2584, 2598, 2600, 2652, 2665, 2691, 2708, 2781, 2789, 2798, 2809, 2827, 2846, 2855, 2859, 2903, 3051 ]
> #Set(ords);
379
> #Set([o : o in ords | o le 100]);
53
> C := HyperellipticCurve([x^3 + x + 1, x^5 - x ]);
> Csim,phi := SimplifiedModel(C);
> Csim;
Hyperelliptic Curve defined by y^2 = x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 - 2*x + 1 over Rational Field
> Q := C![0,-1];
> origin := C![0,0];
> phi(Q);
(0 : -1 : 1)
> phi(origin);
(0 : 1 : 1)
> Q := phi(Q);
> origin := phi(origin);
> C := Csim;
> 
> 
> C;
Hyperelliptic Curve defined by y^2 = x^6 + 4*x^5 + 2*x^4 + 2*x^3 + x^2 - 2*x + 1 over Rational Field
> Q;
(0 : -1 : 1)
> origin;
(0 : 1 : 1)
> CC := ChangeRing(C,GF(19));
> J := Jacobian(CC);
> Qtilde := J![CC!Q,CC!origin];
> Qtilde;
(x^2, x + 18, 2)
> Order(Qtilde);
123
> function order(p) CC := ChangeRing(C,GF(19)); J := Jacobian(CC);  return Order(J![CC!Q,CC!origin]); end function;
> order(19);
123
> order(7);
123
> function order(p) CC := ChangeRing(C,GF(p)); J := Jacobian(CC);  return Order(J![CC!Q,CC!origin]); end function;
> order(7);
61
> Discriminant(CC);
1
> Discriminant(C);
4707057664
> factor($1);
[ <2, 20>, <67, 2> ]
> P := [p : p in [2..3000] | IsPrime(p) and p ne 2 and p ne 67];
> time ords := [order(p) : p in P];


[Interrupted]
> 
>> time ords := [Order(ChangeRing(E,GF(p))!Q) : p in P];
                                          ^
Runtime error in '!': Illegal coercion
> quit;

Total time: 928.700 seconds
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[was@modular hsia]$ exit
exit

Process magma finished