ALGORITHMS FOR MODULAR ELLIPTIC CURVES

Final errata list to the First Edition text, last updated 22 August 1996

(The changes on pages 4–5 are a minimal set which makes the text correct; however, this material will be rewritten for a future edition in such a way as to make the discussion on duality clearer.)

Page  Line  Correction
1  9  Change “2447” to “2463” and “5089” to “5113”.
2  10  Change “L^{(r)}(f, 1)” to “L^{(r)}(f, 1)/r!”.
4  −8  Change “dim_{ℂ} H_{1}(X_{G}, ℂ)” to “dim_{ℝ} H_{1}(X_{G}, ℝ)”.
5  5  In (2.1.1) change “H_{1}(X_{G}, ℂ)” to “H_{1}(X_{G}, ℝ)”.
5  8  Change “an isomorphism of complex vector spaces” to “a vector space iso-

morphism”.

5  9  In (2.1.2) change “H_{1}^{+}(X_{G}, ℂ)” to “H_{1}(X_{G}, ℝ)”.
5  11  Change “H_{1}^{+}(X_{G})” to “H_{1}(X_{G})”.
5  −16  Change “H_{1}(X_{Γ}, ℂ)” to “H_{1}(X_{G}, ℝ)”.
6  −8  Change “group ring” to “group algebra”.
6  −7  Change “ℤΓ” to “ℚΓ”, twice.
6  −6  Change “free abelian group on” to “ℚ-vector space generated by”.
8  −3  In (2.2.4) change “[b/d] − [a/c]” to “[a/c] − [b/d]”.
17  −6  Change “q^{α}w” to “q^{α+β−i}w” in the matrix.
22  6  Change “finite” to “infinite”.

23 head Change “2.10” to “2.9”. 36 display Correct 3-term relations by changing all signs (the resulting system is equiv-

alent to the one printed).

37  −13  Change “(0 : 1)” to “(1 : 1)”.
37  −12  Change “(0)” to “(1)”.
39  5  Change “exp(−2π/11)” to “exp(−2π/\sqrt{11})”.
41  9  Change “-6” to “−6”.
41  −1  Change “1 + p − 3n_{2}(p)” to “1 + p + 3n_{2}(p)”.
48  11  Change last two congruences “ (mod 16)” to “ (mod 32)”.
48  22  Change “b_{2}^{3}” to “b_{2}^{2}”.
48  23  Change “c_{4}” to “c_{6}”.
53  14  Change “a_{2}” to “a_{3}”.
54  4  Change “4, 8, 12 or 16” to “4, 8 or 12”.
58  10  In line 5 change “H” to “log(H)”.
58  −5  Change “on” to “on an”.
59  −18  Add right parenthesis after first “exp(B)”.
60  −12  Change “log^{+}(x) = max{1, log |x|}” to “log^{+}(x) = log max{1, |x|}”.

60  −9  Change “log(|Δ|” to “log |Δ|”.
60  −7  Change “1.946” to “1.922”.
61  2  Change “1.946” to “1.922”.
64  16  Change “d_{1} must have the same sign as −c + \sqrt{d′}”
to “either d_{1} > 0 or c + \sqrt{d′} > 0”.

66  −5  In line 4 change d1*(-c+sqrt(d'))<0
             to d1<0 AND (c+sqrt(d'))<0.

68  25  In line 10 before “THEN” insert “AND even(l)”.
68  27  In line 12 before “THEN” insert “AND (gxodd=1)”.
68  −7  Change “to to” to “to”.
70  −2  Delete “divide… Δ;”. Add sentence: “Note that since (c_{4}, c_{6}) are invariants

of a minimal equation, it follows that (I, J) is p-reduced for all p ≥ 3.”

71  −3  Change “b^{2}” to “3b^{2}” in both places.
72  3, 6  Change “λ^{2}′” to “λ′^{2}” and “p^{2}′” to “p′^{2}”.
72  4, 5  Insert “)” before “/6a”.
72  −9  Change “<” to “≤”.
72  −5  Change “as it” to “as it is”.
74  14  In program line 18 change “x13” to “x1”.
75  3  In program line 5 change “4*t*w^{3}” to “4*v*w^{3}”.
75  4  In program line 5 change “u^{2}*v” to “u^{3}*v”.
76  −12  Change “−c + d^{2}/(4q^{2})” to “(−c + d^{2}/(4q^{2}), 0)”.
77  −10  Change second “\sqrt{e_{3} − e_{1}}” to “\sqrt{e_{3} − e_{2}}”.
77  −2  Change “if are” to “if we are”.
79  3  Change “a_{2}x” to “2a_{2}x”.
80  −6  Change “2447” to “2463”.
81  2  Change “5089/2447” to “5113/2463”.
84  4  Change “2447” to “2463” and “5089” to “5113”.
86  2  Change “L^{(r)}(E, 1) = L^{(r)}(f, 1)” to “L^{(r)}(E, 1)/r! = L^{(r)}(f, 1)/r!”.
86  4  Change “L^{(r)}(E, 1)/ΩR” to “L^{(r)}(E, 1)/r!ΩR”.
86  6  Change “L^{(r)}(f, 1)” to “L^{(r)}(f, 1)/r!”.
87  20  Change “reults” to “results”.
292  6  Change “L^{(r)}(f, 1)” to “L^{(r)}(f, 1)/r!”, and

“L^{(r)}(E, 1)/ΩR” to “L^{(r)}(E, 1)/r!ΩR”.

292  9  Change “L^{(r)}(f, 1)” to “L^{(r)}(f, 1)/r!”.
293–340  1  Change “L^{(r)}(1)” to “L^{(r)}(1)/r!”, and

“L^{(r)}(1)/ΩR” to “L^{(r)}(1)/r!ΩR”.

343  −1  Add “(1971)”.

JEC

22 August 1996