Atkin-Lehner |
2+ 3- 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168x |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
21 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
169199699926032 = 24 · 37 · 193 · 893 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 2 -5 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-14084,144447] |
[a1,a2,a3,a4,a6] |
Generators |
[133:801:1] |
Generators of the group modulo torsion |
j |
19311349076038912/10574981245377 |
j-invariant |
L |
6.4118205692348 |
L(r)(E,1)/r! |
Ω |
0.49823944386244 |
Real period |
R |
0.61280734141972 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000897 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584u1 |
Quadratic twists by: -4 |