Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
27456bt |
Isogeny class |
Conductor |
27456 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-1790949822824448 = -1 · 234 · 36 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11- 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-147265,21896161] |
[a1,a2,a3,a4,a6] |
Generators |
[232:405:1] |
Generators of the group modulo torsion |
j |
-1347365318848849/6831931392 |
j-invariant |
L |
3.0670368323601 |
L(r)(E,1)/r! |
Ω |
0.47290473616771 |
Real period |
R |
3.2427639202924 |
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 |
27456ba1 6864x1 82368dw1 |
Quadratic twists by: -4 8 -3 |