Atkin-Lehner |
31- 61- |
Signs for the Atkin-Lehner involutions |
Class |
58621d |
Isogeny class |
Conductor |
58621 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-54137724541 = -1 · 316 · 61 |
Discriminant |
Eigenvalues |
-1 2 -3 1 5 -1 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1942,-35600] |
[a1,a2,a3,a4,a6] |
Generators |
[1686:7312:27] |
Generators of the group modulo torsion |
j |
-912673/61 |
j-invariant |
L |
4.6530481522165 |
L(r)(E,1)/r! |
Ω |
0.35820678225599 |
Real period |
R |
3.2474595561104 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995989 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61a1 |
Quadratic twists by: -31 |