Atkin-Lehner |
3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117r |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-669400299221166513 = -1 · 37 · 78 · 11 · 136 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 11+ 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,191614,-22570518] |
[a1,a2,a3,a4,a6] |
Generators |
[153:3134:1] [13054:537987:8] |
Generators of the group modulo torsion |
j |
221115865823/190238433 |
j-invariant |
L |
6.0905332519406 |
L(r)(E,1)/r! |
Ω |
0.15827440761777 |
Real period |
R |
19.240423473133 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999948937 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39039h3 693d4 |
Quadratic twists by: -3 13 |