Atkin-Lehner |
2+ 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712k |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
5120 |
Modular degree for the optimal curve |
Δ |
-925903872 = -1 · 210 · 35 · 612 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 2 -2 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,243,243] |
[a1,a2,a3,a4,a6] |
j |
1543313408/904203 |
j-invariant |
L |
4.7622841299526 |
L(r)(E,1)/r! |
Ω |
0.95245682599051 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11712t1 1464a1 35136p1 |
Quadratic twists by: -4 8 -3 |