# Properties

 Label 2.173.abu_bhk 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: $1 - 46 x + 868 x^{2} - 7958 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.0714610774504$, $\pm0.218377440981$ Angle rank: $2$ (numerical) Number field: 4.0.7466816.1 Galois group: $D_{4}$ Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=16x^6+88x^5+46x^4+67x^3+41x^2+88x+44$
• $y^2=26x^6+93x^5+68x^4+16x^3+135x^2+124x+102$
• $y^2=42x^6+82x^5+10x^4+18x^3+151x^2+29x+26$
• $y^2=134x^6+74x^5+42x^4+36x^3+118x^2+159x+2$
• $y^2=63x^6+101x^5+23x^4+91x^3+24x^2+30x+162$
• $y^2=154x^6+73x^5+170x^4+128x^3+93x^2+8x+58$
• $y^2=35x^6+44x^5+152x^4+5x^3+126x^2+3x+70$
• $y^2=5x^6+73x^5+10x^4+145x^3+88x^2+166x+134$
• $y^2=38x^6+62x^5+36x^4+12x^3+167x^2+60x+48$
• $y^2=154x^6+61x^5+147x^4+58x^3+131x^2+67x+94$
• $y^2=109x^6+146x^5+52x^4+7x^3+9x^2+50x+16$
• $y^2=114x^6+101x^5+21x^4+86x^3+111x^2+63x+131$
• $y^2=135x^6+93x^5+168x^4+141x^3+27x^2+68x+66$
• $y^2=36x^6+21x^5+171x^4+129x^3+152x^2+49x+90$
• $y^2=26x^6+77x^5+61x^4+153x^3+87x^2+56x+164$
• $y^2=12x^6+36x^5+161x^4+77x^3+144x^2+106x+33$
• $y^2=168x^6+80x^5+73x^4+152x^3+94x^2+111x+166$
• $y^2=72x^6+63x^5+86x^4+130x^3+81x^2+66x+162$
• $y^2=105x^6+36x^5+159x^4+38x^3+82x^2+149x+137$
• $y^2=25x^6+90x^5+109x^4+154x^3+46x^2+120x+134$
• $y^2=55x^6+97x^5+59x^4+9x^3+107x^2+148x+53$
• $y^2=26x^6+154x^5+81x^4+120x^3+45x^2+3x+107$
• $y^2=8x^6+59x^5+149x^4+132x^3+143x^2+169x+17$
• $y^2=72x^6+33x^5+45x^4+109x^3+168x^2+95x+31$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22794 884452788 26801372680650 802375204879051344 24013871929302929582154 718709349463788606310530900 21510249243189466990979511275466 643780250598982334844643192786351104 19267699138874008421826284855087239870650 576662967580529295698774574975578609780713428

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29550 5176292 895762934 154964305588 26808756847470 4637914314309376 802359177621304414 138808137863182853696 24013807852544738922750

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.7466816.1.
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.bu_bhk $2$ (not in LMFDB)