Atkin-Lehner |
2- 3+ 5+ 7+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
117810ch |
Isogeny class |
Conductor |
117810 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
2064384 |
Modular degree for the optimal curve |
Δ |
457592889600000000 = 214 · 33 · 58 · 72 · 11 · 173 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 11- 2 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-563378,-159331919] |
[a1,a2,a3,a4,a6] |
Generators |
[-479:911:1] |
Generators of the group modulo torsion |
j |
732417776327284737507/16947884800000000 |
j-invariant |
L |
9.8154344598358 |
L(r)(E,1)/r! |
Ω |
0.1745065130583 |
Real period |
R |
2.0088145892724 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000038621 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117810i1 |
Quadratic twists by: -3 |