Atkin-Lehner |
3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
117117b |
Isogeny class |
Conductor |
117117 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
672768 |
Modular degree for the optimal curve |
Δ |
-623062168639911 = -1 · 33 · 72 · 118 · 133 |
Discriminant |
Eigenvalues |
1 3+ -2 7+ 11+ 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-190293,-31925880] |
[a1,a2,a3,a4,a6] |
Generators |
[556:5546:1] [7854:211743:8] |
Generators of the group modulo torsion |
j |
-12846937564867743/10503585169 |
j-invariant |
L |
11.532191596164 |
L(r)(E,1)/r! |
Ω |
0.11428584803158 |
Real period |
R |
25.226639590735 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000148 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117117e1 117117i1 |
Quadratic twists by: -3 13 |