Properties

Label 2.163.abr_bds
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:  $1 - 43 x + 772 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.00500927175908$, $\pm0.260180428357$
Angle rank:  $2$ (numerical)
Number field:  4.0.236600.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20290 697854260 18751268000440 498311180689949600 13239603851228302684750 351763695299335694989288640 9346014118307211732706004205790 248314264261141718132981620834601600 6597461721633703840598094361800562988440 175287960537109662687564594846850091671216500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26265 4329802 705911433 115063337931 18755359303170 3057125037700897 498311411551609233 81224760507406380046 13239635966863229242825

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.236600.1.
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.br_bds$2$(not in LMFDB)