Atkin-Lehner |
2- 3- 5+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
67320bf |
Isogeny class |
Conductor |
67320 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
32717520 = 24 · 37 · 5 · 11 · 17 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 11- -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8418,297277] |
[a1,a2,a3,a4,a6] |
Generators |
[54:13:1] [69:212:1] |
Generators of the group modulo torsion |
j |
5655916189696/2805 |
j-invariant |
L |
8.8132934648145 |
L(r)(E,1)/r! |
Ω |
1.6995324542445 |
Real period |
R |
5.1857164850606 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999359 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22440k1 |
Quadratic twists by: -3 |