Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696br |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1081344 |
Modular degree for the optimal curve |
Δ |
-6.7192218104476E+19 |
Discriminant |
Eigenvalues |
2+ 3- -1 0 11- 1 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,974292,-136102736] |
[a1,a2,a3,a4,a6] |
Generators |
[1662:77936:1] |
Generators of the group modulo torsion |
j |
9987164/6561 |
j-invariant |
L |
5.340614489206 |
L(r)(E,1)/r! |
Ω |
0.11152081305745 |
Real period |
R |
5.98611858024 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000361 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696fz1 8712x1 23232bo1 69696bs1 |
Quadratic twists by: -4 8 -3 -11 |