Atkin-Lehner |
2- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
4004a |
Isogeny class |
Conductor |
4004 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3168 |
Modular degree for the optimal curve |
Δ |
-55989629696 = -1 · 28 · 76 · 11 · 132 |
Discriminant |
Eigenvalues |
2- -1 -3 7+ 11+ 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2717,-54791] |
[a1,a2,a3,a4,a6] |
Generators |
[72:343:1] |
Generators of the group modulo torsion |
j |
-8667872124928/218709491 |
j-invariant |
L |
2.2516945473134 |
L(r)(E,1)/r! |
Ω |
0.3301312177678 |
Real period |
R |
1.705151183928 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16016n1 64064e1 36036j1 100100g1 |
Quadratic twists by: -4 8 -3 5 |