Atkin-Lehner |
2+ 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
81600c |
Isogeny class |
Conductor |
81600 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-68451041280000000 = -1 · 234 · 3 · 57 · 17 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-128033,21707937] |
[a1,a2,a3,a4,a6] |
Generators |
[5066:111475:8] |
Generators of the group modulo torsion |
j |
-56667352321/16711680 |
j-invariant |
L |
4.1701311760301 |
L(r)(E,1)/r! |
Ω |
0.32903296413719 |
Real period |
R |
6.3369504427636 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001161 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81600hu1 2550h1 16320bb1 |
Quadratic twists by: -4 8 5 |