Atkin-Lehner |
2+ 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
27328a |
Isogeny class |
Conductor |
27328 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
28655484928 = 226 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 1 0 7+ 5 0 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-833,4127] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:116:1] |
Generators of the group modulo torsion |
j |
244140625/109312 |
j-invariant |
L |
6.3475591411996 |
L(r)(E,1)/r! |
Ω |
1.0604814132057 |
Real period |
R |
2.9927724626554 |
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 |
27328z1 854c1 |
Quadratic twists by: -4 8 |