Atkin-Lehner |
2- 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
6864s |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-3415965696 = -1 · 215 · 36 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -3 -5 11- 13- 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,208,2496] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:16:1] [2:54:1] |
Generators of the group modulo torsion |
j |
241804367/833976 |
j-invariant |
L |
3.8357468667001 |
L(r)(E,1)/r! |
Ω |
0.9992976881792 |
Real period |
R |
0.47980533129339 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
858j1 27456cb1 20592bj1 75504bq1 |
Quadratic twists by: -4 8 -3 -11 |