Atkin-Lehner |
2- 3+ 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168bz |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
59171472 = 24 · 37 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 6 -1 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9554,362643] |
[a1,a2,a3,a4,a6] |
Generators |
[57:3:1] |
Generators of the group modulo torsion |
j |
6028439354943232/3698217 |
j-invariant |
L |
2.5112811306311 |
L(r)(E,1)/r! |
Ω |
1.6302313181669 |
Real period |
R |
1.5404446610875 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000889 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20292f1 |
Quadratic twists by: -4 |