Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828c |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
436852724151888 = 24 · 36 · 11 · 237 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11+ 6 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-49373,4117638] |
[a1,a2,a3,a4,a6] |
Generators |
[721:18515:1] |
Generators of the group modulo torsion |
j |
5619712000/184437 |
j-invariant |
L |
6.9876669739205 |
L(r)(E,1)/r! |
Ω |
0.52606315299806 |
Real period |
R |
2.2138238647382 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987427 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3036d1 |
Quadratic twists by: -23 |