Atkin-Lehner |
2+ 3- 5- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
31680bj |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-131383296000 = -1 · 217 · 36 · 53 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 5- 1 11+ 6 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2412,48816] |
[a1,a2,a3,a4,a6] |
Generators |
[22:-80:1] |
Generators of the group modulo torsion |
j |
-16241202/1375 |
j-invariant |
L |
6.8874428585082 |
L(r)(E,1)/r! |
Ω |
1.0182368024412 |
Real period |
R |
0.56367396087658 |
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 |
31680dz1 3960o1 3520h1 |
Quadratic twists by: -4 8 -3 |