Atkin-Lehner |
2- 3- 5+ 23- 31- |
Signs for the Atkin-Lehner involutions |
Class |
128340l |
Isogeny class |
Conductor |
128340 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6635520 |
Modular degree for the optimal curve |
Δ |
540336259458000 = 24 · 312 · 53 · 232 · 312 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 -4 0 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-144615468,669376150517] |
[a1,a2,a3,a4,a6] |
Generators |
[232153376:-672709221:32768] |
Generators of the group modulo torsion |
j |
28676123576461325935722496/46325125125 |
j-invariant |
L |
4.915389493362 |
L(r)(E,1)/r! |
Ω |
0.23599341833706 |
Real period |
R |
10.414251284881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999452366 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42780e1 |
Quadratic twists by: -3 |