Atkin-Lehner |
3- 19+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
4047b |
Isogeny class |
Conductor |
4047 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
912 |
Modular degree for the optimal curve |
Δ |
-18684999 = -1 · 36 · 192 · 71 |
Discriminant |
Eigenvalues |
1 3- 2 -4 2 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-170,-889] |
[a1,a2,a3,a4,a6] |
Generators |
[27:106:1] |
Generators of the group modulo torsion |
j |
-538757027353/18684999 |
j-invariant |
L |
5.2083311398061 |
L(r)(E,1)/r! |
Ω |
0.66020570881101 |
Real period |
R |
2.6296506630668 |
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 |
64752j1 12141d1 101175d1 76893a1 |
Quadratic twists by: -4 -3 5 -19 |