Atkin-Lehner |
3- 19+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
15219c |
Isogeny class |
Conductor |
15219 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8128512 |
Modular degree for the optimal curve |
Δ |
-1.075963383109E+25 |
Discriminant |
Eigenvalues |
2 3- -1 -1 -5 2 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1392186063,-19994362666943] |
[a1,a2,a3,a4,a6] |
j |
-409343623062978363908240429056/14759442841001398216731 |
j-invariant |
L |
2.4221462943828 |
L(r)(E,1)/r! |
Ω |
0.012357889257055 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
49 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073e1 |
Quadratic twists by: -3 |