Atkin-Lehner |
2+ 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312y |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-36944833536 = -1 · 210 · 310 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 -4 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,491,8411] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:51:1] [14:135:1] |
Generators of the group modulo torsion |
j |
12758024192/36078939 |
j-invariant |
L |
11.231621146919 |
L(r)(E,1)/r! |
Ω |
0.81239225067558 |
Real period |
R |
2.7650734338491 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999963308 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117312bx1 7332b1 |
Quadratic twists by: -4 8 |