Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312x |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-4633831094976 = -1 · 26 · 34 · 197 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -3 3 0 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-103727,-12824271] |
[a1,a2,a3,a4,a6] |
j |
-40992251392/1539 |
j-invariant |
L |
0.53205346961098 |
L(r)(E,1)/r! |
Ω |
0.13301336408489 |
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 |
69312bx1 34656bg1 3648t1 |
Quadratic twists by: -4 8 -19 |