Atkin-Lehner |
2+ 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312bk |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
132 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
-19180575337218048 = -1 · 220 · 311 · 133 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 -1 3 13- -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,52671,4787487] |
[a1,a2,a3,a4,a6] |
Generators |
[219:5184:1] [-51:1404:1] |
Generators of the group modulo torsion |
j |
61643918316527/73168088292 |
j-invariant |
L |
12.727177787905 |
L(r)(E,1)/r! |
Ω |
0.25796688085133 |
Real period |
R |
0.37376121012331 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999985492 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cf1 3666k1 |
Quadratic twists by: -4 8 |