Atkin-Lehner |
2- 3- 5+ 17- 61- |
Signs for the Atkin-Lehner involutions |
Class |
31110x |
Isogeny class |
Conductor |
31110 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
62208 |
Modular degree for the optimal curve |
Δ |
5199003648000 = 218 · 32 · 53 · 172 · 61 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 0 4 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-4331,561] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:97:1] |
Generators of the group modulo torsion |
j |
8984512774936369/5199003648000 |
j-invariant |
L |
10.245617922122 |
L(r)(E,1)/r! |
Ω |
0.6471544378683 |
Real period |
R |
0.87954429787793 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
93330s1 |
Quadratic twists by: -3 |