Atkin-Lehner |
2- 31- 43- |
Signs for the Atkin-Lehner involutions |
Class |
85312w |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
359424 |
Modular degree for the optimal curve |
Δ |
5292939454447616 = 231 · 31 · 433 |
Discriminant |
Eigenvalues |
2- 0 -1 0 -3 1 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-200108,-34276144] |
[a1,a2,a3,a4,a6] |
Generators |
[-272:172:1] [661:11057:1] |
Generators of the group modulo torsion |
j |
3380470452981441/20190961664 |
j-invariant |
L |
9.7281290276177 |
L(r)(E,1)/r! |
Ω |
0.22580818061045 |
Real period |
R |
7.1802307319678 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999222 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312a1 21328j1 |
Quadratic twists by: -4 8 |