Atkin-Lehner |
2- 5+ 7+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
51520bo |
Isogeny class |
Conductor |
51520 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1133568 |
Modular degree for the optimal curve |
Δ |
-9538928000000 = -1 · 210 · 56 · 72 · 233 |
Discriminant |
Eigenvalues |
2- 1 5+ 7+ -6 1 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-10531241,-13157801905] |
[a1,a2,a3,a4,a6] |
Generators |
[254167294:10620908375:54872] |
Generators of the group modulo torsion |
j |
-126142795384287538429696/9315359375 |
j-invariant |
L |
5.3191569209542 |
L(r)(E,1)/r! |
Ω |
0.04190343908739 |
Real period |
R |
10.578202801461 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51520k1 12880x1 |
Quadratic twists by: -4 8 |