Atkin-Lehner |
7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12397l |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
10209462571 = 79 · 11 · 23 |
Discriminant |
Eigenvalues |
1 -1 -1 7- 11- 7 -6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-11802508,-15611564359] |
[a1,a2,a3,a4,a6] |
j |
4505721246665691247/253 |
j-invariant |
L |
0.65162233386714 |
L(r)(E,1)/r! |
Ω |
0.081452791733393 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111573t1 12397k1 |
Quadratic twists by: -3 -7 |