Atkin-Lehner |
2- 3+ 5- 89- |
Signs for the Atkin-Lehner involutions |
Class |
21360j |
Isogeny class |
Conductor |
21360 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
14336 |
Modular degree for the optimal curve |
Δ |
2050560000 = 212 · 32 · 54 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 -4 -6 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-400,-2048] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:30:1] [-8:24:1] |
Generators of the group modulo torsion |
j |
1732323601/500625 |
j-invariant |
L |
6.6508853367815 |
L(r)(E,1)/r! |
Ω |
1.0908802304613 |
Real period |
R |
0.76210077319504 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1335b1 85440bk1 64080q1 106800bx1 |
Quadratic twists by: -4 8 -3 5 |