Atkin-Lehner |
2- 3+ 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
9744n |
Isogeny class |
Conductor |
9744 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
Δ |
2263920648192 = 213 · 34 · 76 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- -4 0 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3920,62016] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:216:1] [-32:392:1] |
Generators of the group modulo torsion |
j |
1626794704081/552715002 |
j-invariant |
L |
4.398377925926 |
L(r)(E,1)/r! |
Ω |
0.75481852966849 |
Real period |
R |
0.48558889245623 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1218j2 38976bz2 29232bs2 68208dc2 |
Quadratic twists by: -4 8 -3 -7 |