Atkin-Lehner |
2+ 3- 5- 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
47970t |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
116736 |
Modular degree for the optimal curve |
Δ |
-20192335897500 = -1 · 22 · 37 · 54 · 133 · 412 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 -4 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4914,254848] |
[a1,a2,a3,a4,a6] |
Generators |
[-698:1285:8] [-58:614:1] |
Generators of the group modulo torsion |
j |
-18003268247329/27698677500 |
j-invariant |
L |
7.0983210258181 |
L(r)(E,1)/r! |
Ω |
0.61379347484935 |
Real period |
R |
0.24093069427662 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999976 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15990o1 |
Quadratic twists by: -3 |