Atkin-Lehner |
2- 7- 11+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
8162k |
Isogeny class |
Conductor |
8162 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-10218684974891008 = -1 · 232 · 7 · 112 · 532 |
Discriminant |
Eigenvalues |
2- -2 -2 7- 11+ 0 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-239889,45464233] |
[a1,a2,a3,a4,a6] |
Generators |
[-214:9435:1] |
Generators of the group modulo torsion |
j |
-1526703943653102339217/10218684974891008 |
j-invariant |
L |
3.8846882027411 |
L(r)(E,1)/r! |
Ω |
0.40906888239855 |
Real period |
R |
0.29676299410471 |
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 |
65296o1 73458q1 57134r1 89782e1 |
Quadratic twists by: -4 -3 -7 -11 |