Atkin-Lehner |
2+ 3+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192a |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
512 |
Modular degree for the optimal curve |
Δ |
172368 = 24 · 34 · 7 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 4 -6 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-47,-108] |
[a1,a2,a3,a4,a6] |
j |
733001728/10773 |
j-invariant |
L |
1.8217734478846 |
L(r)(E,1)/r! |
Ω |
1.8217734478846 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6384k1 25536bc1 9576w1 79800bt1 |
Quadratic twists by: -4 8 -3 5 |