Atkin-Lehner |
3- 11+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
8151d |
Isogeny class |
Conductor |
8151 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
4320 |
Modular degree for the optimal curve |
Δ |
160436133 = 310 · 11 · 13 · 19 |
Discriminant |
Eigenvalues |
-2 3- 0 -5 11+ 13+ 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-198,-952] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:13:1] |
Generators of the group modulo torsion |
j |
862801408000/160436133 |
j-invariant |
L |
2.0194292645441 |
L(r)(E,1)/r! |
Ω |
1.2885311172496 |
Real period |
R |
0.15672336022855 |
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 |
24453g1 89661m1 105963t1 |
Quadratic twists by: -3 -11 13 |