Atkin-Lehner |
2- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696bw |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
21938176 = 214 · 13 · 103 |
Discriminant |
Eigenvalues |
2- 1 -1 0 -6 13+ 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-81,143] |
[a1,a2,a3,a4,a6] |
Generators |
[1:8:1] |
Generators of the group modulo torsion |
j |
3631696/1339 |
j-invariant |
L |
5.7772077012957 |
L(r)(E,1)/r! |
Ω |
1.9632937512747 |
Real period |
R |
1.471304967466 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006239 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696f1 21424t1 |
Quadratic twists by: -4 8 |