Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12144v |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-2.0978464946312E+21 |
Discriminant |
Eigenvalues |
2- 3+ 2 -4 11+ -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2654992,-2761128512] |
[a1,a2,a3,a4,a6] |
Generators |
[32266:5788134:1] |
Generators of the group modulo torsion |
j |
-505304979693115442833/512169554353324032 |
j-invariant |
L |
3.6359086999779 |
L(r)(E,1)/r! |
Ω |
0.056821543426212 |
Real period |
R |
5.3323506085026 |
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 |
1518s1 48576dz1 36432cg1 |
Quadratic twists by: -4 8 -3 |