Atkin-Lehner |
2- 31+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
23312h |
Isogeny class |
Conductor |
23312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
1564441837568 = 230 · 31 · 47 |
Discriminant |
Eigenvalues |
2- -2 4 0 4 6 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3216,35092] |
[a1,a2,a3,a4,a6] |
j |
898352786449/381943808 |
j-invariant |
L |
3.056008083842 |
L(r)(E,1)/r! |
Ω |
0.76400202096053 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2914h1 93248y1 |
Quadratic twists by: -4 8 |