Atkin-Lehner |
7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12397m |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-2582994030463 = -1 · 79 · 112 · 232 |
Discriminant |
Eigenvalues |
1 2 -4 7- 11- -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,2523,-58960] |
[a1,a2,a3,a4,a6] |
j |
43986977/64009 |
j-invariant |
L |
0.86055940355595 |
L(r)(E,1)/r! |
Ω |
0.43027970177797 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111573x1 12397n1 |
Quadratic twists by: -3 -7 |