Atkin-Lehner |
2+ 3+ 5+ 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
51150i |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
4955156250000 = 24 · 3 · 510 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 11- 4 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-11775,475125] |
[a1,a2,a3,a4,a6] |
Generators |
[101:523:1] |
Generators of the group modulo torsion |
j |
11556972012529/317130000 |
j-invariant |
L |
4.3368894687441 |
L(r)(E,1)/r! |
Ω |
0.76590664236788 |
Real period |
R |
2.8312128586203 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999988 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10230bc1 |
Quadratic twists by: 5 |