Atkin-Lehner |
2+ 3- 17- 23- |
Signs for the Atkin-Lehner involutions |
Class |
18768f |
Isogeny class |
Conductor |
18768 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-1751279616 = -1 · 211 · 37 · 17 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -3 -2 -4 -4 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-192,2196] |
[a1,a2,a3,a4,a6] |
Generators |
[78:-684:1] [-4:54:1] |
Generators of the group modulo torsion |
j |
-384200066/855117 |
j-invariant |
L |
6.8947653395011 |
L(r)(E,1)/r! |
Ω |
1.3227207192622 |
Real period |
R |
0.18616297127729 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9384c1 75072cm1 56304k1 |
Quadratic twists by: -4 8 -3 |