Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312n |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-135497855048193216 = -1 · 26 · 38 · 199 |
Discriminant |
Eigenvalues |
2+ 3+ 1 1 -5 4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-135495,26163729] |
[a1,a2,a3,a4,a6] |
j |
-91368216064/45001899 |
j-invariant |
L |
1.2232523955987 |
L(r)(E,1)/r! |
Ω |
0.30581309909265 |
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 |
69312bp1 34656n1 3648p1 |
Quadratic twists by: -4 8 -19 |