Atkin-Lehner |
2- 13+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
69056m |
Isogeny class |
Conductor |
69056 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
4073472 |
Modular degree for the optimal curve |
Δ |
-9.1272883738522E+21 |
Discriminant |
Eigenvalues |
2- 1 -3 1 -6 13+ -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,4920863,1865755039] |
[a1,a2,a3,a4,a6] |
Generators |
[4245:315068:1] |
Generators of the group modulo torsion |
j |
50269842484372470023/34817842002305024 |
j-invariant |
L |
4.1980183011356 |
L(r)(E,1)/r! |
Ω |
0.082069122091865 |
Real period |
R |
4.2626855205207 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000147 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69056b1 17264d1 |
Quadratic twists by: -4 8 |