Atkin-Lehner |
2+ 7- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
68614i |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
27 |
Product of Tamagawa factors cp |
deg |
1033344 |
Modular degree for the optimal curve |
Δ |
-273806472939790336 = -1 · 213 · 79 · 134 · 29 |
Discriminant |
Eigenvalues |
2+ -2 1 7- 3 13+ 5 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,158687,6479124] |
[a1,a2,a3,a4,a6] |
Generators |
[534:15339:1] |
Generators of the group modulo torsion |
j |
15473133995901959/9586725707776 |
j-invariant |
L |
3.3430379919424 |
L(r)(E,1)/r! |
Ω |
0.1912654097002 |
Real period |
R |
0.64735292229921 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001584 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68614r1 |
Quadratic twists by: 13 |