Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
6992n |
Isogeny class |
Conductor |
6992 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-928873216 = -1 · 28 · 193 · 232 |
Discriminant |
Eigenvalues |
2- 0 1 1 1 4 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3992,-97092] |
[a1,a2,a3,a4,a6] |
Generators |
[198:2622:1] |
Generators of the group modulo torsion |
j |
-27482443554816/3628411 |
j-invariant |
L |
4.4452216219616 |
L(r)(E,1)/r! |
Ω |
0.30030909544065 |
Real period |
R |
1.2335128731946 |
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 |
1748c1 27968z1 62928bk1 |
Quadratic twists by: -4 8 -3 |