Sample Table with Annotations
924A
The first line of each table indicates the isogeny class of elliptic
curves being considered (using the notation of Cremona's Algorithms
for Modular Elliptic Curves).
0 -1 0 25158 -775719
The second line gives the coefficients
a1 , a2 , a3 , a4 , a6 for
the representative, E, of the isogeny class of elliptic curves used in
the computation of the eigenform.
10 independent ternary forms in M(924,2).
The third line notes the number of classes of ternary quadratic
forms in the appropriate genus associated to E.
1 : 6 77 462 0 0 0
-1 : 17 83 164 -52 -8 -10
1 : 21 110 110 -88 0 0
-1 : 24 83 117 6 12 24
3 : 33 84 98 -84 0 0
-1 : 35 66 98 0 -28 0
1 : 35 41 164 32 28 14
-5 : 41 68 83 -20 -26 -8
-4 : 54 54 77 0 0 -24
6 : 54 62 83 16 36 48
In the body of the table, the last six columns give the
coefficients of the reduced ternary form in each class of
the genus. These are presented in order as a, b, c, r, s, t
for f(x,y,z) = ax2 + by2 + cz2 + ryz + sxz + txy. The
column at left (preceding the colon) provides the scalars
for a linear combination of the genus which is an eigenvector
under all Hecke operators of the form T(p) for all odd
primes not dividing the conductor of E.
In this example, if f1(x,y,z) = 6x2 + 77y2 + 462z2,
. . ., f10(x,y,z) = 54x2 + 62y2 + 83z2 + 16yz + 36xz + 48xy,
then g = f1 - f2 + f3 + . . . -4f9 + 6f10 is an eigenvector
under T(p) for all p not equal to 2, 3, 7, or 11. Each eigenvalue
is a rational integer, and they are the same as the eigenvalues
of the weight two newform associated to E for small primes.
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