Atkin-Lehner |
3+ 5+ 11- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
11715b |
Isogeny class |
Conductor |
11715 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-156570975 = -1 · 36 · 52 · 112 · 71 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 0 11- -4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,134,134] |
[a1,a2,a3,a4,a6] |
Generators |
[4:25:1] [19:90:1] |
Generators of the group modulo torsion |
j |
265971760991/156570975 |
j-invariant |
L |
3.5197575050381 |
L(r)(E,1)/r! |
Ω |
1.1073929637675 |
Real period |
R |
1.5892088988277 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
35145m1 58575s1 128865b1 |
Quadratic twists by: -3 5 -11 |