Atkin-Lehner |
2- 5+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
86240ba |
Isogeny class |
Conductor |
86240 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192000 |
Modular degree for the optimal curve |
Δ |
-75891200000 = -1 · 212 · 55 · 72 · 112 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- 11+ 4 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-68161,-6826735] |
[a1,a2,a3,a4,a6] |
Generators |
[133945:1747460:343] |
Generators of the group modulo torsion |
j |
-174494569592896/378125 |
j-invariant |
L |
4.9006705058352 |
L(r)(E,1)/r! |
Ω |
0.14773553976185 |
Real period |
R |
8.2929783036795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004337 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86240bi1 86240bp1 |
Quadratic twists by: -4 -7 |