Atkin-Lehner |
2- 3- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bm |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1797120 |
Modular degree for the optimal curve |
Δ |
108878926892254992 = 24 · 312 · 115 · 433 |
Discriminant |
Eigenvalues |
2- 3- 0 -5 11+ -4 -6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4258065,3381907763] |
[a1,a2,a3,a4,a6] |
Generators |
[1042:8739:1] |
Generators of the group modulo torsion |
j |
732003337727529952000/9334613073753 |
j-invariant |
L |
3.0659065951131 |
L(r)(E,1)/r! |
Ω |
0.30405521576812 |
Real period |
R |
5.0416938036447 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001647 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17028r1 22704x1 |
Quadratic twists by: -4 -3 |