Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cx |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
-1178314711428096 = -1 · 210 · 310 · 117 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 11- 6 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,2904,1650440] |
[a1,a2,a3,a4,a6] |
Generators |
[418:8712:1] |
Generators of the group modulo torsion |
j |
2048/891 |
j-invariant |
L |
4.3267745632806 |
L(r)(E,1)/r! |
Ω |
0.37867174146356 |
Real period |
R |
1.4282735182837 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991739 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696gq1 8712j1 23232q1 6336q1 |
Quadratic twists by: -4 8 -3 -11 |