Atkin-Lehner |
2+ 3+ 5+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
58560a |
Isogeny class |
Conductor |
58560 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
694811575416960000 = 210 · 314 · 54 · 613 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -2 6 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-229741,13790941] |
[a1,a2,a3,a4,a6] |
Generators |
[-1075308:-6498025:2197] |
Generators of the group modulo torsion |
j |
1309607540948125696/678526929118125 |
j-invariant |
L |
5.0959232985102 |
L(r)(E,1)/r! |
Ω |
0.25200480077758 |
Real period |
R |
10.110766307916 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000472 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58560df1 7320p1 |
Quadratic twists by: -4 8 |