Atkin-Lehner |
2- 3- 5+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85140f |
Isogeny class |
Conductor |
85140 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
3755057130000 = 24 · 38 · 54 · 113 · 43 |
Discriminant |
Eigenvalues |
2- 3- 5+ -3 11+ -4 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4233,-50443] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:225:1] |
Generators of the group modulo torsion |
j |
719152519936/321935625 |
j-invariant |
L |
3.8744501798424 |
L(r)(E,1)/r! |
Ω |
0.61712402430725 |
Real period |
R |
1.569558964142 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006419 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28380c1 |
Quadratic twists by: -3 |