Atkin-Lehner |
3+ 7+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
122199f |
Isogeny class |
Conductor |
122199 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
253440 |
Modular degree for the optimal curve |
Δ |
239374032513 = 3 · 72 · 11 · 236 |
Discriminant |
Eigenvalues |
-1 3+ 2 7+ 11- 6 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-17997,-936486] |
[a1,a2,a3,a4,a6] |
Generators |
[-3333890:2382276:42875] |
Generators of the group modulo torsion |
j |
4354703137/1617 |
j-invariant |
L |
4.222390751555 |
L(r)(E,1)/r! |
Ω |
0.41220103498879 |
Real period |
R |
10.243522850392 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000072689 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
231a1 |
Quadratic twists by: -23 |