Properties

Label 2.163.abr_bdu
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:  $1 - 43 x + 774 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0454082012476$, $\pm0.255772555956$
Angle rank:  $2$ (numerical)
Number field:  4.0.3616137.2
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
$A(\F_{q^r})$ 20292 697963632 18752386950864 498317257603379904 13239626907721710336972 351763763877435395334336768 9346014290026579591660408387548 248314264650588240593719661136268032 6597461722514290287178463869579678891728 175287960539272409287448688902285197849362672

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26269 4330060 705920041 115063538311 18755362959622 3057125093871109 498311412333141649 81224760518247734836 13239635967026583175309

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.3616137.2.
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_bdu$2$(not in LMFDB)