Atkin-Lehner |
2+ 7+ 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
61712a |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
267264 |
Modular degree for the optimal curve |
Δ |
-441771029504 = -1 · 210 · 72 · 192 · 293 |
Discriminant |
Eigenvalues |
2+ 3 3 7+ 1 3 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-20611,1139378] |
[a1,a2,a3,a4,a6] |
j |
-945629354786148/431417021 |
j-invariant |
L |
7.4070364446146 |
L(r)(E,1)/r! |
Ω |
0.92587955491944 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30856c1 |
Quadratic twists by: -4 |