Atkin-Lehner |
2- 31+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
33232i |
Isogeny class |
Conductor |
33232 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
60480 |
Modular degree for the optimal curve |
Δ |
-2139708784 = -1 · 24 · 313 · 672 |
Discriminant |
Eigenvalues |
2- -2 -1 -5 4 0 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-19546,-1058349] |
[a1,a2,a3,a4,a6] |
Generators |
[15268:180029:64] |
Generators of the group modulo torsion |
j |
-51617816773406464/133731799 |
j-invariant |
L |
2.5992063239627 |
L(r)(E,1)/r! |
Ω |
0.20188458820091 |
Real period |
R |
6.4373569749059 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8308d1 |
Quadratic twists by: -4 |