Atkin-Lehner |
2+ 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
39872w |
Isogeny class |
Conductor |
39872 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
4572839936 = 220 · 72 · 89 |
Discriminant |
Eigenvalues |
2+ -2 2 7- 0 4 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-5857,-174465] |
[a1,a2,a3,a4,a6] |
Generators |
[2003:89600:1] |
Generators of the group modulo torsion |
j |
84778086457/17444 |
j-invariant |
L |
4.6118922974545 |
L(r)(E,1)/r! |
Ω |
0.54573264320968 |
Real period |
R |
4.2254136295854 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999975 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39872bd1 1246f1 |
Quadratic twists by: -4 8 |