Atkin-Lehner |
2+ 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312w |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
-70854075482112 = -1 · 232 · 33 · 13 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 2 -3 -3 13+ -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-864417,-309626433] |
[a1,a2,a3,a4,a6] |
j |
-272492272338400297/270286848 |
j-invariant |
L |
0.93944144778288 |
L(r)(E,1)/r! |
Ω |
0.078286822529051 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312bv1 3666e1 |
Quadratic twists by: -4 8 |