Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192j |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-233941298492223216 = -1 · 24 · 312 · 317 |
Discriminant |
Eigenvalues |
2+ 3- 1 -3 -4 2 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-833187,293649887] |
[a1,a2,a3,a4,a6] |
Generators |
[527:-961:1] |
Generators of the group modulo torsion |
j |
-6179217664/22599 |
j-invariant |
L |
4.9520384628311 |
L(r)(E,1)/r! |
Ω |
0.31484422638847 |
Real period |
R |
0.98303344314298 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000213 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064h1 2232b1 |
Quadratic twists by: -3 -31 |