Atkin-Lehner |
2- 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
23312r |
Isogeny class |
Conductor |
23312 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
183523999744 = 217 · 313 · 47 |
Discriminant |
Eigenvalues |
2- -3 -3 -3 -2 -4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7339,241114] |
[a1,a2,a3,a4,a6] |
Generators |
[-75:608:1] [-38:682:1] |
Generators of the group modulo torsion |
j |
10672703078913/44805664 |
j-invariant |
L |
3.5316031662673 |
L(r)(E,1)/r! |
Ω |
1.0163920986851 |
Real period |
R |
0.28955386827223 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2914e1 93248bo1 |
Quadratic twists by: -4 8 |