Atkin-Lehner |
2- 7- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
89012r |
Isogeny class |
Conductor |
89012 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
705024 |
Modular degree for the optimal curve |
Δ |
183020659931076352 = 28 · 7 · 114 · 178 |
Discriminant |
Eigenvalues |
2- -1 -2 7- 11+ 0 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-165404,-15653000] |
[a1,a2,a3,a4,a6] |
Generators |
[-214:3146:1] [482:4046:1] |
Generators of the group modulo torsion |
j |
280241872/102487 |
j-invariant |
L |
8.4577063034836 |
L(r)(E,1)/r! |
Ω |
0.24398883470406 |
Real period |
R |
1.9257953872231 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000186 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89012j1 |
Quadratic twists by: 17 |