Atkin-Lehner |
3- 31+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
23157d |
Isogeny class |
Conductor |
23157 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13248 |
Modular degree for the optimal curve |
Δ |
1569975129 = 39 · 312 · 83 |
Discriminant |
Eigenvalues |
1 3- -2 -4 -4 4 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-513,-3920] |
[a1,a2,a3,a4,a6] |
Generators |
[-122:169:8] [-12:26:1] |
Generators of the group modulo torsion |
j |
20503329553/2153601 |
j-invariant |
L |
7.6332083980059 |
L(r)(E,1)/r! |
Ω |
1.0098809903533 |
Real period |
R |
3.7792613540217 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7719b1 |
Quadratic twists by: -3 |