Atkin-Lehner |
2- 3+ 7+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82992br |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-36884775341232 = -1 · 24 · 33 · 72 · 136 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 0 13- 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13473,-664632] |
[a1,a2,a3,a4,a6] |
Generators |
[1322:10101:8] |
Generators of the group modulo torsion |
j |
-16905533974528000/2305298458827 |
j-invariant |
L |
4.9201209837468 |
L(r)(E,1)/r! |
Ω |
0.21989717175726 |
Real period |
R |
3.7291073705265 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20748u1 |
Quadratic twists by: -4 |