Atkin-Lehner |
2- 3- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42588i |
Isogeny class |
Conductor |
42588 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-1398658420072368 = -1 · 24 · 37 · 72 · 138 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 0 13+ -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-44616,-4049071] |
[a1,a2,a3,a4,a6] |
Generators |
[520:-10647:1] |
Generators of the group modulo torsion |
j |
-174456832/24843 |
j-invariant |
L |
4.2846835811202 |
L(r)(E,1)/r! |
Ω |
0.16296021766913 |
Real period |
R |
1.0955341438552 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14196b1 3276j1 |
Quadratic twists by: -3 13 |