Atkin-Lehner |
2- 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69192bd |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
72000 |
Modular degree for the optimal curve |
Δ |
689404732416 = 210 · 36 · 314 |
Discriminant |
Eigenvalues |
2- 3- -1 3 5 1 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2883,44206] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:302:1] |
Generators of the group modulo torsion |
j |
3844 |
j-invariant |
L |
7.4248667987423 |
L(r)(E,1)/r! |
Ω |
0.8473731989303 |
Real period |
R |
4.3811078801266 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000349 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7688a1 69192bh1 |
Quadratic twists by: -3 -31 |