Atkin-Lehner |
2+ 7+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
21112a |
Isogeny class |
Conductor |
21112 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
-7386159872 = -1 · 28 · 7 · 132 · 293 |
Discriminant |
Eigenvalues |
2+ -1 0 7+ -4 13+ -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-393,-4979] |
[a1,a2,a3,a4,a6] |
Generators |
[25:14:1] [85:-754:1] |
Generators of the group modulo torsion |
j |
-26288512000/28852187 |
j-invariant |
L |
6.1234539224344 |
L(r)(E,1)/r! |
Ω |
0.51386388888452 |
Real period |
R |
0.49652041903289 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42224c1 |
Quadratic twists by: -4 |