Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696eq |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
260770151043072 = 212 · 33 · 119 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 11- 0 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-643236,-198563904] |
[a1,a2,a3,a4,a6] |
Generators |
[-464:16:1] |
Generators of the group modulo torsion |
j |
150229394496/1331 |
j-invariant |
L |
4.4430993668756 |
L(r)(E,1)/r! |
Ω |
0.16858044655008 |
Real period |
R |
3.2944948962572 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001647 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ep1 34848bk1 69696em1 6336bs1 |
Quadratic twists by: -4 8 -3 -11 |