Atkin-Lehner |
2- 3+ 5+ 7- 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
117810cl |
Isogeny class |
Conductor |
117810 |
Conductor |
∏ cp |
864 |
Product of Tamagawa factors cp |
deg |
5308416 |
Modular degree for the optimal curve |
Δ |
1.0205010675194E+21 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 11+ -4 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2685743,-711914569] |
[a1,a2,a3,a4,a6] |
Generators |
[-329:11826:1] |
Generators of the group modulo torsion |
j |
79351136961745545522387/37796335834051379200 |
j-invariant |
L |
9.3236582163432 |
L(r)(E,1)/r! |
Ω |
0.12359946908949 |
Real period |
R |
3.1431021415922 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000077724 |
(Analytic) order of Ш |
t |
6 |
Number of elements in the torsion subgroup |
Twists |
117810r3 |
Quadratic twists by: -3 |