Atkin-Lehner |
3+ 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117a |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
338688 |
Modular degree for the optimal curve |
Δ |
-773462755212147 = -1 · 33 · 73 · 113 · 137 |
Discriminant |
Eigenvalues |
0 3+ 0 7+ 11+ 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,5070,-1330833] |
[a1,a2,a3,a4,a6] |
Generators |
[117:929:1] |
Generators of the group modulo torsion |
j |
110592000/5934929 |
j-invariant |
L |
4.0295286763487 |
L(r)(E,1)/r! |
Ω |
0.24130029603333 |
Real period |
R |
2.0874035256311 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999179616 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117117d2 9009b1 |
Quadratic twists by: -3 13 |