Atkin-Lehner |
3- 5- 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
13065p |
Isogeny class |
Conductor |
13065 |
Conductor |
∏ cp |
21 |
Product of Tamagawa factors cp |
deg |
21168 |
Modular degree for the optimal curve |
Δ |
-916387265625 = -1 · 3 · 57 · 13 · 673 |
Discriminant |
Eigenvalues |
-1 3- 5- -3 1 13- -1 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-8565,307842] |
[a1,a2,a3,a4,a6] |
Generators |
[89:458:1] |
Generators of the group modulo torsion |
j |
-69487867377124561/916387265625 |
j-invariant |
L |
3.5164597964557 |
L(r)(E,1)/r! |
Ω |
0.88755050277315 |
Real period |
R |
0.18866584602757 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39195l1 65325d1 |
Quadratic twists by: -3 5 |