Properties

Label 2.163.abu_bgu
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
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.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19878 695054148 18745614367038 498317561750990544 13239688202999662862238 351764028851636602829476836 9346014996759719715956816285574 248314265953992534556905732024972288 6597461723930601469548592797805709926422 175287960538842415394931453502414310626585188

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

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.1159488.4.
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
2.163.bu_bgu$2$(not in LMFDB)