# Properties

 Label 2.173.abu_bhl 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: $1 - 46 x + 869 x^{2} - 7958 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.0814447409702$, $\pm0.214601179315$ Angle rank: $2$ (numerical) Number field: 4.0.6884928.2 Galois group: $D_{4}$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

• $y^2=81x^6+157x^5+87x^4+160x^3+37x^2+135x+69$
• $y^2=14x^6+85x^5+6x^4+3x^3+28x^2+111x+5$
• $y^2=113x^6+11x^5+25x^4+137x^3+126x^2+70x+114$
• $y^2=55x^6+93x^5+162x^4+145x^3+34x^2+8x+94$
• $y^2=71x^6+18x^5+25x^4+27x^3+118x^2+156x+58$
• $y^2=24x^6+35x^5+98x^4+151x^3+170x^2+16x+103$
• $y^2=x^6+129x^5+20x^4+129x^3+86x^2+138x+44$
• $y^2=128x^6+123x^5+77x^4+153x^3+67x^2+86x+70$
• $y^2=5x^6+26x^5+43x^4+155x^3+77x^2+150x+57$
• $y^2=41x^6+128x^5+8x^4+108x^3+73x^2+126x+120$
• $y^2=26x^6+7x^5+73x^4+149x^3+112x^2+46x+37$
• $y^2=147x^6+54x^5+30x^4+82x^3+26x^2+131x+13$
• $y^2=41x^6+9x^5+98x^4+167x^3+15x^2+80x+146$
• $y^2=78x^6+171x^5+110x^4+37x^3+120x^2+76x+49$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22795 884514385 26802088280620 802379675022474025 24013891603602758580475 718709417137242875727596560 21510249433142056662099751928995 643780251038565996840205091571436425 19267699139694550249337142266201659392460 576662967581659487556949296418471603368923425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29552 5176430 895767924 154964432548 26808759371774 4637914355265844 802359178169168356 138808137869094191750 24013807852591803172832

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.6884928.2.
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.bu_bhl $2$ (not in LMFDB)