Atkin-Lehner |
2+ 3- 5+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
10680c |
Isogeny class |
Conductor |
10680 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
12096 |
Modular degree for the optimal curve |
Δ |
-11211436800 = -1 · 28 · 39 · 52 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -4 -4 -6 -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1361,19539] |
[a1,a2,a3,a4,a6] |
Generators |
[-17879:-1041930:6859] [-26:195:1] |
Generators of the group modulo torsion |
j |
-1089876235264/43794675 |
j-invariant |
L |
6.1180053326537 |
L(r)(E,1)/r! |
Ω |
1.2668508031001 |
Real period |
R |
0.067073641251936 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21360b1 85440i1 32040n1 53400p1 |
Quadratic twists by: -4 8 -3 5 |