Atkin-Lehner |
3- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
3069a |
Isogeny class |
Conductor |
3069 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
54720 |
Modular degree for the optimal curve |
Δ |
2813357232935412273 = 39 · 115 · 316 |
Discriminant |
Eigenvalues |
-1 3- 2 -2 11+ 4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-904694,-320999844] |
[a1,a2,a3,a4,a6] |
j |
112331320422638310937/3859200593875737 |
j-invariant |
L |
1.2410220760309 |
L(r)(E,1)/r! |
Ω |
0.15512775950386 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49104bs1 1023a1 76725o1 33759i1 |
Quadratic twists by: -4 -3 5 -11 |