Atkin-Lehner |
2+ 3- 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
8670k |
Isogeny class |
Conductor |
8670 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
1768680000 = 26 · 32 · 54 · 173 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 0 2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2038,-35512] |
[a1,a2,a3,a4,a6] |
Generators |
[-26:20:1] |
Generators of the group modulo torsion |
j |
190407092777/360000 |
j-invariant |
L |
3.9432344961511 |
L(r)(E,1)/r! |
Ω |
0.71067880941138 |
Real period |
R |
0.69356832579142 |
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 |
69360cr1 26010bh1 43350bz1 8670b1 |
Quadratic twists by: -4 -3 5 17 |