Atkin-Lehner |
2+ 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192g |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
94080 |
Modular degree for the optimal curve |
Δ |
4339002922836599808 = 210 · 37 · 710 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ -6 -2 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4955392,-4246324048] |
[a1,a2,a3,a4,a6] |
Generators |
[-1276:912:1] |
Generators of the group modulo torsion |
j |
13141891860831409148932/4237307541832617 |
j-invariant |
L |
4.1675142908357 |
L(r)(E,1)/r! |
Ω |
0.10119019829316 |
Real period |
R |
1.9611885816591 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6384d1 25536d1 9576x1 79800bj1 |
Quadratic twists by: -4 8 -3 5 |