Properties

Label 2.173.abs_bfg
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 44 x + 812 x^{2} - 7612 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0220781886823$, $\pm0.264129150942$
Angle rank:  $2$ (numerical)
Number field:  4.0.80128.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 23086 886456228 26804419010782 802360384340108944 24013758275941299367726 718708928234079160588207396 21510248178942243006572291744158 643780248715341027973514713889968128 19267699136818589340025647932482557377806 576662967579592495153581821660283840542517988

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 130 29618 5176882 895746390 154963572170 26808741135074 4637914084842602 802359175273675870 138808137848375227042 24013807852505728010738

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.80128.1.
All geometric endomorphisms are defined over $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.bs_bfg$2$(not in LMFDB)