Atkin-Lehner |
2+ 3- 5+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
85680m |
Isogeny class |
Conductor |
85680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1548288 |
Modular degree for the optimal curve |
Δ |
39510114005250000 = 24 · 313 · 56 · 73 · 172 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -2 4 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2256798,1304894747] |
[a1,a2,a3,a4,a6] |
j |
108981872598107416576/3387355453125 |
j-invariant |
L |
0.6777778432902 |
L(r)(E,1)/r! |
Ω |
0.33888894079337 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42840bu1 28560r1 |
Quadratic twists by: -4 -3 |