Properties

Label 1.167.av
Base Field $\F_{167}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{167}$
Dimension:  $1$
L-polynomial:  $1 - 21 x + 167 x^{2}$
Frobenius angles:  $\pm0.198098183086$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-227}) \)
Galois group:  $C_2$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 147 27783 4658724 777840651 129892706097 21691969323696 3622557628545807 604967116551667443 101029508516904717708 16871927924669774730543

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 27783 4658724 777840651 129892706097 21691969323696 3622557628545807 604967116551667443 101029508516904717708 16871927924669774730543

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{167}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-227}) \).
All geometric endomorphisms are defined over $\F_{167}$.

Base change

This is a primitive isogeny class.

Twists

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