Atkin-Lehner |
3- 7+ 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
8463i |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
88704 |
Modular degree for the optimal curve |
Δ |
39349833794415417 = 3 · 7 · 133 · 318 |
Discriminant |
Eigenvalues |
1 3- -2 7+ 4 13- 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-308802,65330239] |
[a1,a2,a3,a4,a6] |
j |
3256581892696035537817/39349833794415417 |
j-invariant |
L |
2.1898229563782 |
L(r)(E,1)/r! |
Ω |
0.36497049272971 |
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 |
25389h1 59241d1 110019v1 |
Quadratic twists by: -3 -7 13 |