Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
12936g |
Isogeny class |
Conductor |
12936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-38355981569136 = -1 · 24 · 37 · 77 · 113 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7- 11- -1 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2140,294813] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:539:1] |
Generators of the group modulo torsion |
j |
575511296/20376279 |
j-invariant |
L |
4.5168838909515 |
L(r)(E,1)/r! |
Ω |
0.48944016280656 |
Real period |
R |
0.76905619831896 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25872n1 103488da1 38808cc1 1848f1 |
Quadratic twists by: -4 8 -3 -7 |