ALGORITHMS FOR MODULAR ELLIPTIC CURVES

Errata list to the Second (1997) Edition text, last updated 4 September 1998

Page  Line  Correction
6  13  For “17583” read “17598”, and for “31570” read “31586”.
6  16  Delete “most of”, and after “5077” insert “(and beyond, as they become

available)”.

6 18–25 Delete this whole paragraph, since the computations are now complete to

5077 (and almost complete to 6000, in fact).

26 −10 For “of β + 1 forms g_{i}(z) = g(q^{i}z)” read “of dimension β + 1, spanned by the forms g_{i}(z) = q^{i}g(q^{i}z)”. [Then we have g_{i} = g |( \begin{matrix}q^{i} & 0 \\ 0 & 1 \end{matrix} ); otherwise there would be many missing powers of q in the proof.]

36  −10  For “(e^{2πib/d} − εe^{2πic/d})” read “(e^{2πinb/d} − εe^{2πinc/d})”.
64  −17  For “\frac{1}{2}p < a ≤ \frac{1}{2}p” read “−\frac{1}{2}p < a ≤ \frac{1}{2}p”.
90  −3  For “these are elliptic curves, which are twists of E” read “these are also

elliptic curves, isomorphic to E over ℚ”.

95  23  Denominator of d should be 8a^{2}, not 8a.
108  23  Delete the sentence starting “At present”, since the computations are now

complete to 5077 (and almost complete to 6000, in fact).

108 Table The line for 3001–4000 should read: 3837 1665 2006 166 0.

The line for 4001–5000 should read: 3962 1690 2092 180 0. The line for 1–5077 should read: 17598 8035 8959 603 1.

363–373 Running head should say “TABLE 5” and not “TABLE 2”. 372 All entries for N = 912 are wrong; replace as in table below.

curve  degree
912A1 192 = 2^{6} · 3
912B1 96 = 2^{5} · 3
912C1 192 = 2^{6} · 3
912D1 160 = 2^{5} · 5
912E1 288 = 2^{5} · 3^{2}
912F1 480 = 2^{5} · 3 · 5

curve  degree
912G1 96 = 2^{5} · 3
912H1 480 = 2^{5} · 3 · 5
912I1  96 = 2^{5} · 3
912J1  72 = 2^{3} · 3^{2}
912K1 1440 = 2^{5} · 3^{2} · 5
912L1 160 = 2^{5} · 5

Thanks to: Jeremy Bygott, Ian Connell, Michael Young, Blair Kelly III, Jeroen Spandaw, Larry Washington. . ..

JEC

4 September 1998