Atkin-Lehner |
3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117r |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
204474653869655169 = 310 · 72 · 114 · 136 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 11+ 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-431996,107207286] |
[a1,a2,a3,a4,a6] |
Generators |
[-718:7203:1] [-4418:108675:8] |
Generators of the group modulo torsion |
j |
2533811507137/58110129 |
j-invariant |
L |
6.0905332519406 |
L(r)(E,1)/r! |
Ω |
0.31654881523555 |
Real period |
R |
4.8101058682833 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999948937 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
39039h4 693d3 |
Quadratic twists by: -3 13 |