Properties

Label 2.173.abt_bgs
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:  $( 1 - 24 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$
Frobenius angles:  $\pm0.134271185755$, $\pm0.205732831898$
Angle rank:  $2$ (numerical)
Jacobians:  42

This isogeny class is not 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 42 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22950 886099500 26810159430600 802410946623000000 24013991915474321994750 718709688353854105036128000 21510250038097269046508213085150 643780252047529323097499087388000000 19267699140376158772989253203739140385800 576662967578326840345522412071609257111487500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29605 5177988 895802833 154965079869 26808769488490 4637914485702753 802359179426664193 138808137874004628084 24013807852453022716525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ay $\times$ 1.173.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_agc$2$(not in LMFDB)
2.173.d_agc$2$(not in LMFDB)
2.173.bt_bgs$2$(not in LMFDB)