Atkin-Lehner |
2+ 3- 17- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
27234i |
Isogeny class |
Conductor |
27234 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
172805612544 = 210 · 38 · 172 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 -4 4 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-43308,3479760] |
[a1,a2,a3,a4,a6] |
Generators |
[-168:2532:1] |
Generators of the group modulo torsion |
j |
12322709457584833/237044736 |
j-invariant |
L |
2.748156305042 |
L(r)(E,1)/r! |
Ω |
0.93578969398968 |
Real period |
R |
1.468362134512 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9078h1 |
Quadratic twists by: -3 |