Atkin-Lehner |
3- 5- 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
21645m |
Isogeny class |
Conductor |
21645 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
19683140081450625 = 318 · 54 · 133 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5- 4 0 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-69917,2269316] |
[a1,a2,a3,a4,a6] |
Generators |
[21:889:1] |
Generators of the group modulo torsion |
j |
51848800828831369/27000192155625 |
j-invariant |
L |
3.8903335648254 |
L(r)(E,1)/r! |
Ω |
0.33883849987297 |
Real period |
R |
2.8703449919976 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7215f1 108225bc1 |
Quadratic twists by: -3 5 |