Properties

Label 2.173.abx_bkk
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 173 x^{2} )( 1 - 24 x + 173 x^{2} )$
Frobenius angles:  $\pm0.100717649571$, $\pm0.134271185755$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22350 880634700 26787963241800 802349304553368000 24013871780333827581750 718709572018411789590086400 21510250299306336751131068560950 643780253861346979112359495528800000 19267699146428429616792175464416926379400 576662967593089661086977437352335919472123500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 125 29421 5173700 895734017 154964304625 26808765149034 4637914542023125 802359181687269793 138808137917606328500 24013807853067786557061

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.az $\times$ 1.173.ay 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.ab_aju$2$(not in LMFDB)
2.173.b_aju$2$(not in LMFDB)
2.173.bx_bkk$2$(not in LMFDB)