Atkin-Lehner |
2- 3+ 5- 13- 41- |
Signs for the Atkin-Lehner involutions |
Class |
31980d |
Isogeny class |
Conductor |
31980 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
213696 |
Modular degree for the optimal curve |
Δ |
4456827527190480 = 24 · 314 · 5 · 132 · 413 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 -2 13- 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-124345,16609870] |
[a1,a2,a3,a4,a6] |
Generators |
[-174:5740:1] |
Generators of the group modulo torsion |
j |
13288996961861287936/278551720449405 |
j-invariant |
L |
4.7716410324942 |
L(r)(E,1)/r! |
Ω |
0.43582136767876 |
Real period |
R |
3.6495388450156 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127920ch1 95940c1 |
Quadratic twists by: -4 -3 |