Atkin-Lehner |
2+ 3+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
27768a |
Isogeny class |
Conductor |
27768 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
67200 |
Modular degree for the optimal curve |
Δ |
-2055668150016 = -1 · 28 · 35 · 135 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -1 5 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-58300,5438068] |
[a1,a2,a3,a4,a6] |
j |
-85604552312875216/8029953711 |
j-invariant |
L |
1.5825791279629 |
L(r)(E,1)/r! |
Ω |
0.79128956398142 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
55536j1 83304p1 |
Quadratic twists by: -4 -3 |