Atkin-Lehner |
2- 3+ 17+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
85782k |
Isogeny class |
Conductor |
85782 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
999936 |
Modular degree for the optimal curve |
Δ |
-713104003694592 = -1 · 218 · 38 · 17 · 293 |
Discriminant |
Eigenvalues |
2- 3+ 0 3 2 1 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-658158,205244715] |
[a1,a2,a3,a4,a6] |
Generators |
[433:1079:1] |
Generators of the group modulo torsion |
j |
-1292766987789702125/29238755328 |
j-invariant |
L |
10.583252117462 |
L(r)(E,1)/r! |
Ω |
0.46963670789031 |
Real period |
R |
0.31298578289174 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003319 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85782j1 |
Quadratic twists by: 29 |