Atkin-Lehner |
2- 3+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192ba |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
460800 |
Modular degree for the optimal curve |
Δ |
8664492536749008 = 24 · 39 · 317 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 4 -2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-259470,-50674491] |
[a1,a2,a3,a4,a6] |
Generators |
[528679378810:-7772639084209:761048497] |
Generators of the group modulo torsion |
j |
6912000/31 |
j-invariant |
L |
7.0878885187566 |
L(r)(E,1)/r! |
Ω |
0.21158991659201 |
Real period |
R |
16.749116956152 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999989737 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69192a1 2232h1 |
Quadratic twists by: -3 -31 |