Atkin-Lehner |
2+ 3- 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
47040cr |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
354816 |
Modular degree for the optimal curve |
Δ |
-10413167579136000 = -1 · 215 · 32 · 53 · 710 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -5 1 8 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3201,-4911201] |
[a1,a2,a3,a4,a6] |
Generators |
[227:2472:1] |
Generators of the group modulo torsion |
j |
-392/1125 |
j-invariant |
L |
6.3265314586633 |
L(r)(E,1)/r! |
Ω |
0.18417370050852 |
Real period |
R |
4.2938618822809 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040t1 23520bm1 47040z1 |
Quadratic twists by: -4 8 -7 |