Atkin-Lehner |
3- 5+ 31- 37- |
Signs for the Atkin-Lehner involutions |
Class |
51615d |
Isogeny class |
Conductor |
51615 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
31104 |
Modular degree for the optimal curve |
Δ |
-28617678675 = -1 · 36 · 52 · 31 · 373 |
Discriminant |
Eigenvalues |
-1 3- 5+ 1 -2 -3 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1148,17322] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:108:1] [-10:171:1] |
Generators of the group modulo torsion |
j |
-229333309561/39256075 |
j-invariant |
L |
6.0516109412864 |
L(r)(E,1)/r! |
Ω |
1.1366340798958 |
Real period |
R |
0.44367921100861 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5735b1 |
Quadratic twists by: -3 |