Atkin-Lehner |
3- 13- 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
51129j |
Isogeny class |
Conductor |
51129 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
6707200 |
Modular degree for the optimal curve |
Δ |
-85367700209929059 = -1 · 36 · 132 · 195 · 234 |
Discriminant |
Eigenvalues |
0 3- -1 1 3 13- 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-926385138,-10852642128535] |
[a1,a2,a3,a4,a6] |
j |
-120606557357926050532382048256/117102469423771 |
j-invariant |
L |
1.9703081615368 |
L(r)(E,1)/r! |
Ω |
0.013682695567443 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5681d1 |
Quadratic twists by: -3 |