Atkin-Lehner |
5+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
725a |
Isogeny class |
Conductor |
725 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
96 |
Modular degree for the optimal curve |
Δ |
2265625 = 57 · 29 |
Discriminant |
Eigenvalues |
1 0 5+ 2 -6 -2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-67,216] |
[a1,a2,a3,a4,a6] |
Generators |
[8:8:1] |
Generators of the group modulo torsion |
j |
2146689/145 |
j-invariant |
L |
2.6227061923179 |
L(r)(E,1)/r! |
Ω |
2.5453515525219 |
Real period |
R |
2.0607811048493 |
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 |
11600q1 46400k1 6525h1 145a1 |
Quadratic twists by: -4 8 -3 5 |