Atkin-Lehner |
3- 17+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
13617d |
Isogeny class |
Conductor |
13617 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7488 |
Modular degree for the optimal curve |
Δ |
28369671417 = 36 · 173 · 892 |
Discriminant |
Eigenvalues |
1 3- -2 2 -4 2 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1188,13819] |
[a1,a2,a3,a4,a6] |
Generators |
[-242:1291:8] |
Generators of the group modulo torsion |
j |
254478514753/38915873 |
j-invariant |
L |
4.8347330705312 |
L(r)(E,1)/r! |
Ω |
1.1321204876857 |
Real period |
R |
4.2705110658446 |
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 |
1513a1 |
Quadratic twists by: -3 |