Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312m |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1382400 |
Modular degree for the optimal curve |
Δ |
227762065980260352 = 220 · 35 · 197 |
Discriminant |
Eigenvalues |
2+ 3+ 0 4 -4 0 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2206913,1262429889] |
[a1,a2,a3,a4,a6] |
j |
96386901625/18468 |
j-invariant |
L |
1.2197309788091 |
L(r)(E,1)/r! |
Ω |
0.30493274730123 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312di1 2166i1 3648j1 |
Quadratic twists by: -4 8 -19 |