Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12144s |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
9867534336 = 213 · 32 · 11 · 233 |
Discriminant |
Eigenvalues |
2- 3+ -1 -1 11+ 1 7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1056,12672] |
[a1,a2,a3,a4,a6] |
Generators |
[72:-552:1] |
Generators of the group modulo torsion |
j |
31824875809/2409066 |
j-invariant |
L |
3.4848189121846 |
L(r)(E,1)/r! |
Ω |
1.2627964428288 |
Real period |
R |
0.11498352630962 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1518q1 48576dr1 36432bz1 |
Quadratic twists by: -4 8 -3 |