Atkin-Lehner |
2+ 3+ 5+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
128160a |
Isogeny class |
Conductor |
128160 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1308672 |
Modular degree for the optimal curve |
Δ |
-35522316357120000 = -1 · 212 · 39 · 54 · 893 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 -4 -6 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-229608,-43307568] |
[a1,a2,a3,a4,a6] |
Generators |
[8898:262575:8] |
Generators of the group modulo torsion |
j |
-16604795017728/440605625 |
j-invariant |
L |
4.6740339540504 |
L(r)(E,1)/r! |
Ω |
0.10887864263119 |
Real period |
R |
5.3661050940477 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000092427 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128160w1 128160ba1 |
Quadratic twists by: -4 -3 |