Atkin-Lehner |
2+ 3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
27744a |
Isogeny class |
Conductor |
27744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
-45380174524416 = -1 · 212 · 33 · 177 |
Discriminant |
Eigenvalues |
2+ 3+ 1 2 1 -1 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-40845,3207429] |
[a1,a2,a3,a4,a6] |
Generators |
[431:8092:1] |
Generators of the group modulo torsion |
j |
-76225024/459 |
j-invariant |
L |
5.546155904968 |
L(r)(E,1)/r! |
Ω |
0.64246411398596 |
Real period |
R |
2.1581578582493 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27744i1 55488dk1 83232be1 1632e1 |
Quadratic twists by: -4 8 -3 17 |