# Properties

 Label 2.173.aby_blj 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: $( 1 - 25 x + 173 x^{2} )^{2}$ Frobenius angles: $\pm0.100717649571$, $\pm0.100717649571$ Angle rank: $1$ (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:

• $y^2=105x^6+51x^5+148x^4+150x^3+6x^2+163x+163$
• $y^2=26x^6+137x^5+115x^4+13x^3+145x^2+119x+55$
• $y^2=125x^6+57x^5+92x^4+85x^3+25x^2+x+170$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22201 879181801 26781328804624 802326964224789481 24013810603530039138961 718709433924468742544920576 21510250058154373435229667433129 643780253640718644727815368232575625 19267699146964781848315305574009365809296 576662967597000535442693223972804346029302521

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 124 29372 5172418 895709076 154963909844 26808759997958 4637914490027348 802359181412295268 138808137921470311114 24013807853230645957772

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-67})$$$)$
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.a_akt $2$ (not in LMFDB) 2.173.by_blj $2$ (not in LMFDB) 2.173.z_rk $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.a_akt $2$ (not in LMFDB) 2.173.by_blj $2$ (not in LMFDB) 2.173.z_rk $3$ (not in LMFDB) 2.173.a_kt $4$ (not in LMFDB) 2.173.az_rk $6$ (not in LMFDB)