Atkin-Lehner |
2- 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
129712w |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
696960 |
Modular degree for the optimal curve |
Δ |
1882461965778944 = 217 · 118 · 67 |
Discriminant |
Eigenvalues |
2- 0 -3 -5 11- -2 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-65219,-6061374] |
[a1,a2,a3,a4,a6] |
Generators |
[-127:416:1] [-121:242:1] |
Generators of the group modulo torsion |
j |
34941753/2144 |
j-invariant |
L |
6.8368311132025 |
L(r)(E,1)/r! |
Ω |
0.29989615582049 |
Real period |
R |
1.8997773551625 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000006532 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16214b1 129712v1 |
Quadratic twists by: -4 -11 |