Atkin-Lehner |
2+ 3- 5- 19+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
80370s |
Isogeny class |
Conductor |
80370 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
9491536260 = 22 · 312 · 5 · 19 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 -2 -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-999,-10967] |
[a1,a2,a3,a4,a6] |
Generators |
[-21:31:1] [-16:35:1] |
Generators of the group modulo torsion |
j |
151334226289/13019940 |
j-invariant |
L |
7.8364913680934 |
L(r)(E,1)/r! |
Ω |
0.8538131398545 |
Real period |
R |
4.5891138250443 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998366 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
26790p1 |
Quadratic twists by: -3 |