Properties

Label 2.163.abr_bdv
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:  $1 - 43 x + 775 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0560069052587$, $\pm0.253428620168$
Angle rank:  $2$ (numerical)
Number field:  4.0.18688277.1
Galois group:  $D_{4}$
Jacobians:  33

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 33 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20293 698018321 18752946433039 498320291831463101 13239638361756329771248 351763797491349705006361817 9346014371634964391281386721339 248314264824509464971621049581816053 6597461722870375518151378133417817560233 175287960540059999808972877133718159794716416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26271 4330189 705924339 115063637856 18755364751851 3057125120565595 498311412682162803 81224760522631684123 13239635967086070499846

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.18688277.1.
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_bdv$2$(not in LMFDB)