Atkin-Lehner |
3- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
32307k |
Isogeny class |
Conductor |
32307 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
340032 |
Modular degree for the optimal curve |
Δ |
-5048538136612443 = -1 · 37 · 1110 · 89 |
Discriminant |
Eigenvalues |
1 3- -4 4 11- 0 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-183318,-30418313] |
[a1,a2,a3,a4,a6] |
j |
-26266897921/194643 |
j-invariant |
L |
3.2287498824352 |
L(r)(E,1)/r! |
Ω |
0.11531249580132 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96921u1 32307l1 |
Quadratic twists by: -3 -11 |