Atkin-Lehner |
2- 3+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
21648t |
Isogeny class |
Conductor |
21648 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
114048 |
Modular degree for the optimal curve |
Δ |
-1843032263491584 = -1 · 221 · 311 · 112 · 41 |
Discriminant |
Eigenvalues |
2- 3+ -1 4 11- 1 -3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-26256,-2627136] |
[a1,a2,a3,a4,a6] |
Generators |
[1688:68992:1] |
Generators of the group modulo torsion |
j |
-488726621230609/449959048704 |
j-invariant |
L |
4.8349948547929 |
L(r)(E,1)/r! |
Ω |
0.18066174095617 |
Real period |
R |
3.3453367251439 |
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 |
2706p1 86592cu1 64944bg1 |
Quadratic twists by: -4 8 -3 |