Atkin-Lehner |
2+ 5- 7+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
117040j |
Isogeny class |
Conductor |
117040 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
125952 |
Modular degree for the optimal curve |
Δ |
163856000000 = 210 · 56 · 72 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ -2 5- 7+ 11+ -2 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3080,61828] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:30:1] [-24:350:1] |
Generators of the group modulo torsion |
j |
3156580738084/160015625 |
j-invariant |
L |
8.3623639438179 |
L(r)(E,1)/r! |
Ω |
1.0078695337142 |
Real period |
R |
0.69142248922962 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002374 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58520w1 |
Quadratic twists by: -4 |