Atkin-Lehner |
2+ 3- 7+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12558i |
Isogeny class |
Conductor |
12558 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-18890052760680192 = -1 · 28 · 318 · 72 · 132 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ 2 13+ 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1364665,613524188] |
[a1,a2,a3,a4,a6] |
Generators |
[523:6290:1] |
Generators of the group modulo torsion |
j |
-281061535296977850715273/18890052760680192 |
j-invariant |
L |
4.8279192120287 |
L(r)(E,1)/r! |
Ω |
0.36715813272506 |
Real period |
R |
0.36526187233124 |
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 |
100464bf1 37674n1 87906i1 |
Quadratic twists by: -4 -3 -7 |