Atkin-Lehner |
2- 11- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68728d |
Isogeny class |
Conductor |
68728 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
311040 |
Modular degree for the optimal curve |
Δ |
354198820096 = 28 · 117 · 71 |
Discriminant |
Eigenvalues |
2- 0 3 1 11- 5 -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-589996,174430212] |
[a1,a2,a3,a4,a6] |
Generators |
[473:1089:1] |
Generators of the group modulo torsion |
j |
50081212818432/781 |
j-invariant |
L |
8.0602715452855 |
L(r)(E,1)/r! |
Ω |
0.68222749215164 |
Real period |
R |
1.4768298765991 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000113 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6248b1 |
Quadratic twists by: -11 |