Atkin-Lehner |
2- 3- 5- 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
9690x |
Isogeny class |
Conductor |
9690 |
Conductor |
∏ cp |
480 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
117279896371200 = 220 · 36 · 52 · 17 · 192 |
Discriminant |
Eigenvalues |
2- 3- 5- -2 -2 -2 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-12940,-223600] |
[a1,a2,a3,a4,a6] |
Generators |
[-40:500:1] |
Generators of the group modulo torsion |
j |
239623075960954561/117279896371200 |
j-invariant |
L |
7.7031125437208 |
L(r)(E,1)/r! |
Ω |
0.4703964591552 |
Real period |
R |
0.13646489738952 |
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 |
77520bn1 29070m1 48450k1 |
Quadratic twists by: -4 -3 5 |