Atkin-Lehner |
2+ 3- 41- |
Signs for the Atkin-Lehner involutions |
Class |
23616n |
Isogeny class |
Conductor |
23616 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-13221937152 = -1 · 214 · 39 · 41 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 -3 6 7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,240,-5344] |
[a1,a2,a3,a4,a6] |
Generators |
[169:2205:1] |
Generators of the group modulo torsion |
j |
128000/1107 |
j-invariant |
L |
5.1067741133914 |
L(r)(E,1)/r! |
Ω |
0.62373168914557 |
Real period |
R |
4.0937266794854 |
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 |
23616bx1 2952c1 7872a1 |
Quadratic twists by: -4 8 -3 |