Atkin-Lehner |
2- 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8272k |
Isogeny class |
Conductor |
8272 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-2168455168 = -1 · 222 · 11 · 47 |
Discriminant |
Eigenvalues |
2- 2 -2 -1 11+ 1 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,176,-2112] |
[a1,a2,a3,a4,a6] |
Generators |
[21:102:1] |
Generators of the group modulo torsion |
j |
146363183/529408 |
j-invariant |
L |
5.0894529713297 |
L(r)(E,1)/r! |
Ω |
0.74476979802815 |
Real period |
R |
3.4167960252984 |
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 |
1034c1 33088bl1 74448bm1 90992bd1 |
Quadratic twists by: -4 8 -3 -11 |