Atkin-Lehner |
2+ 3- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
32736d |
Isogeny class |
Conductor |
32736 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
18266688 = 26 · 33 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 11+ -2 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-78,144] |
[a1,a2,a3,a4,a6] |
Generators |
[0:12:1] |
Generators of the group modulo torsion |
j |
830584000/285417 |
j-invariant |
L |
6.8035628634247 |
L(r)(E,1)/r! |
Ω |
2.0041143899234 |
Real period |
R |
1.1315992236825 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32736a1 65472bx1 98208z1 |
Quadratic twists by: -4 8 -3 |