Atkin-Lehner |
2- 3- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bp |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4064256 |
Modular degree for the optimal curve |
Δ |
-8.4216416922731E+20 |
Discriminant |
Eigenvalues |
2- 3- -3 1 11+ -4 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-28101819,57355950314] |
[a1,a2,a3,a4,a6] |
Generators |
[2477:54272:1] |
Generators of the group modulo torsion |
j |
-821938895581650775417/282039076306944 |
j-invariant |
L |
4.5883852481241 |
L(r)(E,1)/r! |
Ω |
0.15534141126196 |
Real period |
R |
3.6921780958858 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994789 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8514k1 22704z1 |
Quadratic twists by: -4 -3 |