Properties

Label 2.163.abs_bex
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:  $1 - 44 x + 803 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0842188003801$, $\pm0.226190889167$
Angle rank:  $2$ (numerical)
Number field:  4.0.9697296.3
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
$A(\F_{q^r})$ 20157 697210473 18752322930516 498328865957506329 13239688362053184916557 351763961202073756482829200 9346014746815412685986411240373 248314265423674683863061078771340329 6597461723387866772431797494276617886004 175287960539768526672563310304678046306228553

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26240 4330044 705936484 115064072400 18755373480590 3057125243288880 498311413884553924 81224760529002786372 13239635967064055307200

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.9697296.3.
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.bs_bex$2$(not in LMFDB)