Atkin-Lehner |
3- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
86151f |
Isogeny class |
Conductor |
86151 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
423936 |
Modular degree for the optimal curve |
Δ |
-3339152986971633 = -1 · 3 · 133 · 477 |
Discriminant |
Eigenvalues |
1 3- 0 3 -1 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-67421,7283501] |
[a1,a2,a3,a4,a6] |
Generators |
[-213993:1085219:729] |
Generators of the group modulo torsion |
j |
-3144219625/309777 |
j-invariant |
L |
9.9211077870465 |
L(r)(E,1)/r! |
Ω |
0.43583129232867 |
Real period |
R |
5.6909106559813 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004186 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1833e1 |
Quadratic twists by: -47 |