Atkin-Lehner |
2+ 13+ 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
8398b |
Isogeny class |
Conductor |
8398 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
33792 |
Modular degree for the optimal curve |
Δ |
1731282165392 = 24 · 132 · 173 · 194 |
Discriminant |
Eigenvalues |
2+ 2 -2 2 6 13+ 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-16816,-843984] |
[a1,a2,a3,a4,a6] |
j |
525935106358018057/1731282165392 |
j-invariant |
L |
2.5159541594598 |
L(r)(E,1)/r! |
Ω |
0.4193256932433 |
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 |
67184r1 75582w1 109174q1 |
Quadratic twists by: -4 -3 13 |