# Properties

 Label 2.173.abv_bio 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: $( 1 - 24 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$ Frobenius angles: $\pm0.134271185755$, $\pm0.161302001611$ 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 $A(\F_{q^r})$ 22650 883485900 26800490008800 802389032946072000 24013970554885867223250 718709758864758143080646400 21510250500426649639749763928850 643780253562920817760338094334304000 19267699143792078937748143503941153522400 576662967583061610311515019121461366460619500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 127 29517 5176120 895778369 154964942027 26808772118634 4637914585387511 802359181315333921 138808137898613561080 24013807852650191361957

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ay $\times$ 1.173.ax 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_ahy $2$ (not in LMFDB) 2.173.b_ahy $2$ (not in LMFDB) 2.173.bv_bio $2$ (not in LMFDB)