Properties

Label 2.163.abu_bgu
Base field $\F_{163}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $1 - 46 x + 852 x^{2} - 7498 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0800016625006$, $\pm0.186669006544$
Angle rank:  $2$ (numerical)
Number field:  4.0.1159488.4
Galois group:  $D_{4}$
Jacobians:  $16$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $19878$ $695054148$ $18745614367038$ $498317561750990544$ $13239688202999662862238$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $118$ $26158$ $4328494$ $705920470$ $115064071018$ $18755377087534$ $3057125325046834$ $498311414948783710$ $81224760535684673686$ $13239635966994105402238$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.1159488.4.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.163.bu_bgu$2$(not in LMFDB)