# Properties

 Label 2.173.abv_bij 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: $1 - 47 x + 893 x^{2} - 8131 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.0630646735849$, $\pm0.201502091012$ Angle rank: $2$ (numerical) Number field: 4.0.2863413.1 Galois group: $D_{4}$ Jacobians: 12

This isogeny class is simple and geometrically 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 12 curves, and hence is principally polarizable:

• $y^2=72x^6+107x^5+104x^4+25x^3+20x^2+6x+87$
• $y^2=7x^6+64x^5+75x^4+158x^3+61x^2+87x+127$
• $y^2=86x^6+15x^5+38x^4+142x^3+144x^2+47x+109$
• $y^2=50x^6+44x^5+65x^4+37x^3+64x^2+15x+78$
• $y^2=42x^6+31x^5+147x^4+63x^3+151x^2+31x+134$
• $y^2=43x^6+46x^5+158x^4+24x^3+101x^2+80x+25$
• $y^2=32x^6+18x^5+14x^4+84x^3+162x^2+30x+39$
• $y^2=4x^6+65x^5+133x^4+84x^3+96x^2+158x+128$
• $y^2=19x^6+88x^5+13x^4+150x^3+61x^2+77x+3$
• $y^2=61x^6+169x^5+43x^4+116x^3+129x^2+46x+114$
• $y^2=59x^6+141x^5+16x^4+107x^3+19x^2+45x+64$
• $y^2=20x^6+61x^5+86x^4+151x^3+107x^2+51x+103$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22645 883177645 26796833870065 802365499477709125 24013862943484532473600 718709371604288605548056245 21510249359225606911303901531905 643780250809760580674312082385225125 19267699138667509260125728103605546876045 576662967577654628172930391898626162055065600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 127 29507 5175415 895752099 154964247602 26808757673339 4637914339328411 802359177884002531 138808137861695194795 24013807852425029980982

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.2863413.1.
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.bv_bij $2$ (not in LMFDB)