Properties

Label 1.167.j
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:  $1 + 9 x + 167 x^{2}$
Frobenius angles:  $\pm0.613213937437$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-587}) \)
Galois group:  $C_2$
Jacobians:  7

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 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 177 28143 4653684 777788091 129892690947 21691956622896 3622557513563277 604967118448978323 101029508531315030268 16871927924691376024743

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 177 28143 4653684 777788091 129892690947 21691956622896 3622557513563277 604967118448978323 101029508531315030268 16871927924691376024743

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{167}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-587}) \).
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.aj$2$(not in LMFDB)