Atkin-Lehner |
2- 3+ 11+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
21648m |
Isogeny class |
Conductor |
21648 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
6179958816768 = 222 · 33 · 113 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11+ 2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-490968,-132248592] |
[a1,a2,a3,a4,a6] |
j |
3195392484115617625/1508779008 |
j-invariant |
L |
2.8857332213829 |
L(r)(E,1)/r! |
Ω |
0.18035832633643 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2706g1 86592dg1 64944bq1 |
Quadratic twists by: -4 8 -3 |