Properties

Label 2.163.abr_bdt
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:  $1 - 43 x + 773 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0320302473605$, $\pm0.258019905074$
Angle rank:  $2$ (numerical)
Number field:  4.0.8383413.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20291 697908945 18751827473333 498314220556214925 13239615404212376661296 351763729813505754321128145 9346014205585835766048898284977 248314264462822308637197680052556725 6597461722102269604879099422419500554287 175287960538290331916284594414524812309241600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26267 4329931 705915739 115063438336 18755361143399 3057125066250145 498311411956337251 81224760513175135303 13239635966952406107782

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.8383413.1.
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_bdt$2$(not in LMFDB)