Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
72072bp |
Isogeny class |
Conductor |
72072 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
-469787399091698688 = -1 · 210 · 318 · 72 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11- 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-49971,33255934] |
[a1,a2,a3,a4,a6] |
Generators |
[134:5382:1] |
Generators of the group modulo torsion |
j |
-18486314981572/629323397703 |
j-invariant |
L |
5.0605850361499 |
L(r)(E,1)/r! |
Ω |
0.24653777471442 |
Real period |
R |
5.1316527875892 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001408 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024o1 |
Quadratic twists by: -3 |