Atkin-Lehner |
2- 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312cx |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
29184 |
Modular degree for the optimal curve |
Δ |
-180191232 = -1 · 215 · 32 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 -2 13- -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33,639] |
[a1,a2,a3,a4,a6] |
Generators |
[3:-24:1] |
Generators of the group modulo torsion |
j |
-125000/5499 |
j-invariant |
L |
6.0779350445498 |
L(r)(E,1)/r! |
Ω |
1.4958981590688 |
Real period |
R |
0.50788341887493 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000012178 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cd1 58656c1 |
Quadratic twists by: -4 8 |