Atkin-Lehner |
3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
117117q |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
1010880 |
Modular degree for the optimal curve |
Δ |
-7738410722959917 = -1 · 36 · 7 · 11 · 1310 |
Discriminant |
Eigenvalues |
1 3- 4 7+ 11+ 13+ 3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5355,-4233722] |
[a1,a2,a3,a4,a6] |
j |
-169/77 |
j-invariant |
L |
4.6737122610183 |
L(r)(E,1)/r! |
Ω |
0.18694848419345 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
25 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13013c1 117117bu1 |
Quadratic twists by: -3 13 |