# Properties

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

## Invariants

 Base field: $\F_{173}$ Dimension: $2$ L-polynomial: $( 1 - 26 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$ Frobenius angles: $\pm0.0485897903475$, $\pm0.161302001611$ Angle rank: $2$ (numerical) Jacobians: 3

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 3 curves, and hence is principally polarizable:

• $y^2=58x^6+46x^5+121x^4+23x^3+38x^2+18x+88$
• $y^2=103x^6+130x^5+26x^4+33x^3+24x^2+58x+75$
• $y^2=90x^6+108x^5+136x^4+35x^3+150x^2+5x+128$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22348 880511200 26786438306368 802338869747056000 24013819842264500046748 718709362328292594266675200 21510249575846558479031011278364 643780251671997729825680312313792000 19267699140557827182194136000578810746432 576662967579202210278480231449120091710476000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 125 29417 5173406 895722369 154963969465 26808757327334 4637914386034957 802359178958629921 138808137875313401558 24013807852489475491457

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.aba $\times$ 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ad_ajs $2$ (not in LMFDB) 2.173.d_ajs $2$ (not in LMFDB) 2.173.bx_bki $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ad_ajs $2$ (not in LMFDB) 2.173.d_ajs $2$ (not in LMFDB) 2.173.bx_bki $2$ (not in LMFDB) 2.173.abb_qw $4$ (not in LMFDB) 2.173.at_ju $4$ (not in LMFDB) 2.173.t_ju $4$ (not in LMFDB) 2.173.bb_qw $4$ (not in LMFDB)