Atkin-Lehner |
2+ 3- 103+ |
Signs for the Atkin-Lehner involutions |
Class |
19776o |
Isogeny class |
Conductor |
19776 |
Conductor |
∏ cp |
44 |
Product of Tamagawa factors cp |
deg |
25344 |
Modular degree for the optimal curve |
Δ |
-597889548288 = -1 · 215 · 311 · 103 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 -5 -4 -4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2689,64415] |
[a1,a2,a3,a4,a6] |
Generators |
[-61:72:1] [-7:288:1] |
Generators of the group modulo torsion |
j |
-65645911304/18246141 |
j-invariant |
L |
7.2655177016107 |
L(r)(E,1)/r! |
Ω |
0.87013078830503 |
Real period |
R |
0.18977078449436 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19776g1 9888g1 59328j1 |
Quadratic twists by: -4 8 -3 |