# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)