Properties

Label 1.163.aw
Base Field $\F_{163}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{163}$
Dimension:  $1$
L-polynomial:  $1 - 22 x + 163 x^{2}$
Frobenius angles:  $\pm0.169471200781$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-42}) \)
Galois group:  $C_2$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 142 26412 4330858 705939936 115064218942 18755378227404 3057125333392762 498311414936170368 81224760532425927214 13239635966886006095532

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 26412 4330858 705939936 115064218942 18755378227404 3057125333392762 498311414936170368 81224760532425927214 13239635966886006095532

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-42}) \).
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.163.w$2$(not in LMFDB)