Atkin-Lehner |
2+ 3- 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
77616cj |
Isogeny class |
Conductor |
77616 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
8847360 |
Modular degree for the optimal curve |
Δ |
38662829421689088 = 28 · 39 · 78 · 113 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11- 6 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-258854799,1602996023342] |
[a1,a2,a3,a4,a6] |
j |
87364831012240243408/1760913 |
j-invariant |
L |
2.2669063911487 |
L(r)(E,1)/r! |
Ω |
0.18890886695216 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38808ce1 25872f1 11088p1 |
Quadratic twists by: -4 -3 -7 |