# Properties

 Label 2.173.abw_bjl 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: $( 1 - 25 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$ Frobenius angles: $\pm0.100717649571$, $\pm0.161302001611$ 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:

• $y^2=61x^6+140x^5+42x^4+29x^3+42x^2+140x+61$
• $y^2=162x^6+29x^5+169x^4+118x^3+169x^2+29x+162$
• $y^2=107x^6+82x^5+138x^4+152x^3+138x^2+82x+107$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22499 882028297 26793852469184 802366691511310249 24013909377830444581499 718709620770779195096190976 21510250259274684069083418603107 643780253342292483478066856771740425 19267699144328431169197885890430967316416 576662967586972484667162796438715362456479577

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 126 29468 5174838 895753428 154964547246 26808766967558 4637914533391734 802359181040359396 138808137902477543694 24013807852813050762668

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.az $\times$ 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.ac_aiv $2$ (not in LMFDB) 2.173.c_aiv $2$ (not in LMFDB) 2.173.bw_bjl $2$ (not in LMFDB)