Atkin-Lehner |
2- 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bv |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
2 |
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] |
Generators |
[6251:489004:1] |
Generators of the group modulo torsion |
j |
-272492272338400297/270286848 |
j-invariant |
L |
8.2735196686116 |
L(r)(E,1)/r! |
Ω |
0.51661531786143 |
Real period |
R |
8.0074277193068 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000043135 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312w1 29328z1 |
Quadratic twists by: -4 8 |