Atkin-Lehner |
2- 3+ 7+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
12558k |
Isogeny class |
Conductor |
12558 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-429043266288 = -1 · 24 · 34 · 7 · 132 · 234 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -4 13+ 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,1291,26507] |
[a1,a2,a3,a4,a6] |
Generators |
[81:778:1] |
Generators of the group modulo torsion |
j |
237947646518063/429043266288 |
j-invariant |
L |
4.6066213869171 |
L(r)(E,1)/r! |
Ω |
0.64718662866312 |
Real period |
R |
1.7794795129007 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
100464bz1 37674c1 87906bx1 |
Quadratic twists by: -4 -3 -7 |