Atkin-Lehner |
2+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
50336o |
Isogeny class |
Conductor |
50336 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
522240 |
Modular degree for the optimal curve |
Δ |
-2279723380453376 = -1 · 212 · 117 · 134 |
Discriminant |
Eigenvalues |
2+ -3 1 -4 11- 13- 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,30008,1128688] |
[a1,a2,a3,a4,a6] |
Generators |
[308:6292:1] |
Generators of the group modulo torsion |
j |
411830784/314171 |
j-invariant |
L |
3.2247196829833 |
L(r)(E,1)/r! |
Ω |
0.2953136011356 |
Real period |
R |
0.68247781141722 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000084 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50336ba1 100672z1 4576g1 |
Quadratic twists by: -4 8 -11 |