Atkin-Lehner |
2+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
10192b |
Isogeny class |
Conductor |
10192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
15588021904 = 24 · 78 · 132 |
Discriminant |
Eigenvalues |
2+ 1 -3 7+ 3 13+ 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2172,-39229] |
[a1,a2,a3,a4,a6] |
Generators |
[-214:169:8] |
Generators of the group modulo torsion |
j |
12291328/169 |
j-invariant |
L |
4.3124201295574 |
L(r)(E,1)/r! |
Ω |
0.69988933956921 |
Real period |
R |
3.0807871228698 |
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 |
5096b1 40768cf1 91728p1 10192h1 |
Quadratic twists by: -4 8 -3 -7 |