Atkin-Lehner |
2+ 7+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
52598c |
Isogeny class |
Conductor |
52598 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
156672 |
Modular degree for the optimal curve |
Δ |
33009284210812 = 22 · 7 · 132 · 178 |
Discriminant |
Eigenvalues |
2+ 1 0 7+ -2 13+ 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-18936,962490] |
[a1,a2,a3,a4,a6] |
Generators |
[-45:1335:1] [24:710:1] |
Generators of the group modulo torsion |
j |
107637625/4732 |
j-invariant |
L |
8.0731933485816 |
L(r)(E,1)/r! |
Ω |
0.64940355397596 |
Real period |
R |
1.0359754089161 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52598i1 |
Quadratic twists by: 17 |