Atkin-Lehner |
2- 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
57408ch |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-839535964295528448 = -1 · 228 · 32 · 134 · 233 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 2 13+ -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-329889,85327425] |
[a1,a2,a3,a4,a6] |
Generators |
[-168:11661:1] |
Generators of the group modulo torsion |
j |
-15145674183260713/3202575547392 |
j-invariant |
L |
4.5151529636459 |
L(r)(E,1)/r! |
Ω |
0.2696434017944 |
Real period |
R |
1.3954086933698 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999142 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408bc1 14352bj1 |
Quadratic twists by: -4 8 |