Atkin-Lehner |
2+ 7+ 11- 79- |
Signs for the Atkin-Lehner involutions |
Class |
12166f |
Isogeny class |
Conductor |
12166 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
12289021034752 = 28 · 73 · 116 · 79 |
Discriminant |
Eigenvalues |
2+ 0 -2 7+ 11- -4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-7663,197421] |
[a1,a2,a3,a4,a6] |
Generators |
[23:170:1] |
Generators of the group modulo torsion |
j |
49768215360798537/12289021034752 |
j-invariant |
L |
2.2826968240281 |
L(r)(E,1)/r! |
Ω |
0.66839031695392 |
Real period |
R |
1.1384050936141 |
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 |
97328x1 109494bk1 85162r1 |
Quadratic twists by: -4 -3 -7 |