Atkin-Lehner |
2+ 3- 71- |
Signs for the Atkin-Lehner involutions |
Class |
20448f |
Isogeny class |
Conductor |
20448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-15843948318144 = -1 · 26 · 320 · 71 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 0 -2 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5709,-253460] |
[a1,a2,a3,a4,a6] |
Generators |
[8169967586:-52041163095:73034632] |
Generators of the group modulo torsion |
j |
-441058644928/339590799 |
j-invariant |
L |
6.4863033132848 |
L(r)(E,1)/r! |
Ω |
0.26577780834721 |
Real period |
R |
12.202492287865 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20448i1 40896ba2 6816f1 |
Quadratic twists by: -4 8 -3 |