Atkin-Lehner |
2+ 3- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
12144j |
Isogeny class |
Conductor |
12144 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5120 |
Modular degree for the optimal curve |
Δ |
-3989413296 = -1 · 24 · 34 · 11 · 234 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,121,3036] |
[a1,a2,a3,a4,a6] |
Generators |
[4:60:1] |
Generators of the group modulo torsion |
j |
12144109568/249338331 |
j-invariant |
L |
4.8884990961007 |
L(r)(E,1)/r! |
Ω |
1.0402074992038 |
Real period |
R |
2.3497711273196 |
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 |
6072d1 48576by1 36432l1 |
Quadratic twists by: -4 8 -3 |