Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ci |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-130923856825344 = -1 · 210 · 38 · 117 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 11- -2 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11616,-266200] |
[a1,a2,a3,a4,a6] |
Generators |
[29425:5047515:1] |
Generators of the group modulo torsion |
j |
131072/99 |
j-invariant |
L |
8.1683609698293 |
L(r)(E,1)/r! |
Ω |
0.32697151653181 |
Real period |
R |
6.2454683026886 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000372 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696gj1 4356f1 23232t1 6336ba1 |
Quadratic twists by: -4 8 -3 -11 |