Atkin-Lehner |
2+ 3+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
12384b |
Isogeny class |
Conductor |
12384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-3466727424 = -1 · 212 · 39 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ 3 3 -1 -5 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,324,-1728] |
[a1,a2,a3,a4,a6] |
j |
46656/43 |
j-invariant |
L |
3.0846449177888 |
L(r)(E,1)/r! |
Ω |
0.77116122944719 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12384a1 24768bq1 12384k1 |
Quadratic twists by: -4 8 -3 |