Atkin-Lehner |
2+ 3+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192b |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1536 |
Modular degree for the optimal curve |
Δ |
-2758634928 = -1 · 24 · 33 · 72 · 194 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 0 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,321,-1332] |
[a1,a2,a3,a4,a6] |
j |
227910944768/172414683 |
j-invariant |
L |
0.80190297998182 |
L(r)(E,1)/r! |
Ω |
0.80190297998182 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
6384m1 25536z1 9576u1 79800bs1 |
Quadratic twists by: -4 8 -3 5 |