Abelian variety isogeny class 2.173.abt_bgm over $\F_{173}$

• Label: 2.173.abt_bgm
• Base field: $\F_{173}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 844 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0850578884700$, $\pm0.231907856828$
Angle rank:	$2$ (numerical)
Number field:	4.0.1007325.1
Galois group:	$D_{4}$
Jacobians:	$80$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22944$	$885730176$	$26805959410176$	$802385620086007296$	$24013886477599203154464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$129$	$29593$	$5177178$	$895774561$	$154964399469$	$26808757132102$	$4637914315194513$	$802359177828761953$	$138808137871132700994$	$24013807852720526611153$

Jacobians and polarizations

This isogeny class contains the Jacobians of 80 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=74x^6+69x^5+2x^4+119x^3+147x^2+163x+74$
• $y^2=60x^6+18x^5+116x^4+84x^3+120x^2+11x+80$
• $y^2=77x^6+147x^5+149x^4+132x^3+73x^2+7x+10$
• $y^2=19x^6+24x^5+160x^4+41x^3+84x^2+99x+81$
• $y^2=110x^6+11x^5+62x^4+15x^3+74x^2+39x+43$
• $y^2=21x^6+81x^5+133x^4+x^3+62x^2+100x+101$
• $y^2=155x^6+169x^5+113x^4+78x^3+140x^2+159x+66$
• $y^2=70x^6+37x^5+149x^4+3x^3+169x^2+75x+74$
• $y^2=28x^6+152x^5+78x^4+143x^3+165x^2+157x+15$
• $y^2=27x^6+128x^5+127x^4+86x^3+120x^2+163x+66$
• $y^2=97x^6+163x^5+154x^4+102x^3+77x^2+169x+50$
• $y^2=135x^6+49x^5+143x^4+56x^3+88x^2+59x+77$
• $y^2=32x^6+16x^5+96x^4+22x^3+130x^2+159x+85$
• $y^2=12x^6+92x^5+140x^4+26x^3+17x^2+157x+41$
• $y^2=127x^6+106x^5+18x^4+47x^3+105x^2+165x+74$
• $y^2=123x^6+33x^5+15x^4+85x^3+108x^2+39x+34$
• $y^2=28x^6+71x^5+44x^4+8x^3+51x^2+91x+166$
• $y^2=163x^6+127x^5+88x^4+132x^3+128x^2+168x+158$
• $y^2=147x^6+49x^5+164x^4+60x^3+2x^2+81x+121$
• $y^2=17x^6+152x^5+170x^4+21x^3+142x^2+35x+31$
• and

• $y^2=19x^6+28x^5+72x^4+152x^3+26x^2+74x+80$
• $y^2=144x^6+22x^5+172x^4+168x^3+9x^2+68x+94$
• $y^2=116x^6+4x^5+161x^3+166x^2+170x+18$
• $y^2=121x^6+39x^5+7x^4+159x^3+108x^2+53x+20$
• $y^2=61x^6+171x^5+61x^4+80x^3+155x^2+74x+37$
• $y^2=110x^6+22x^5+137x^4+164x^3+161x^2+2x+144$
• $y^2=62x^6+13x^5+57x^4+155x^3+161x^2+53x+90$
• $y^2=147x^6+158x^5+74x^4+132x^3+101x^2+121x+93$
• $y^2=128x^6+6x^5+90x^4+89x^3+68x^2+71x+139$
• $y^2=152x^6+85x^5+36x^4+46x^3+20x^2+49x+51$
• $y^2=146x^6+170x^5+94x^4+107x^3+4x^2+36x+50$
• $y^2=126x^6+108x^5+23x^4+83x^3+79x^2+66x+92$
• $y^2=17x^6+82x^5+172x^4+133x^3+160x^2+23x+46$
• $y^2=3x^6+53x^5+17x^4+77x^3+87x^2+159x+121$
• $y^2=21x^6+141x^5+123x^4+91x^3+25x^2+4x+128$
• $y^2=3x^6+96x^5+84x^4+14x^3+45x^2+63x+172$
• $y^2=117x^6+18x^5+116x^4+72x^3+117x^2+152x+107$
• $y^2=144x^6+152x^5+81x^4+93x^3+92x^2+115x+28$
• $y^2=18x^6+85x^5+161x^4+78x^3+134x^2+76x+29$
• $y^2=170x^6+128x^5+105x^4+80x^3+22x^2+99x+170$
• $y^2=90x^6+111x^5+67x^4+137x^3+32x^2+52x+131$
• $y^2=151x^6+78x^5+33x^4+149x^3+87x^2+149x+120$
• $y^2=116x^6+48x^5+81x^4+122x^3+50x^2+73x+40$
• $y^2=45x^6+86x^5+78x^4+91x^3+120x^2+31x+20$
• $y^2=93x^6+123x^5+47x^4+153x^3+41x^2+52x+53$
• $y^2=14x^6+139x^5+125x^4+2x^3+124x^2+39x+87$
• $y^2=39x^6+108x^5+82x^4+3x^3+36x^2+97x+87$
• $y^2=71x^6+18x^5+85x^4+111x^3+3x^2+103x+20$
• $y^2=8x^6+62x^5+57x^4+155x^3+12x^2+53x+120$
• $y^2=168x^6+128x^5+150x^4+71x^3+143x^2+87x+160$
• $y^2=107x^6+49x^5+143x^4+7x^3+47x^2+64x+161$
• $y^2=68x^6+134x^5+159x^4+169x^3+97x^2+66x+92$
• $y^2=171x^6+117x^5+15x^4+169x^3+141x^2+125x+62$
• $y^2=143x^6+51x^5+160x^3+164x^2+33x+114$
• $y^2=105x^6+103x^5+147x^4+159x^3+81x^2+63x+121$
• $y^2=133x^5+165x^4+130x^3+138x^2+123x+131$
• $y^2=32x^6+135x^5+148x^4+170x^3+170x^2+164x+75$
• $y^2=93x^6+104x^5+165x^4+50x^3+52x^2+13x+19$
• $y^2=32x^6+75x^5+37x^4+19x^3+93x^2+100x+36$
• $y^2=114x^6+88x^5+70x^4+15x^3+85x^2+96x+61$
• $y^2=74x^6+162x^5+92x^4+31x^3+100x^2+8x+46$
• $y^2=17x^6+x^5+107x^4+97x^3+44x^2+145x+172$
• $y^2=79x^6+90x^5+110x^4+97x^3+64x+26$
• $y^2=91x^6+116x^5+139x^4+111x^3+152x^2+39x+99$
• $y^2=35x^6+32x^5+32x^4+65x^3+120x^2+88x+18$
• $y^2=91x^6+90x^5+77x^4+170x^3+152x^2+44x+94$
• $y^2=59x^6+27x^5+151x^4+154x^3+131x^2+69x+58$
• $y^2=108x^6+107x^5+137x^4+100x^3+171x^2+5x+71$
• $y^2=87x^6+72x^5+124x^4+139x^3+131x^2+145x+142$
• $y^2=89x^6+77x^5+73x^4+137x^3+159x^2+83x+78$
• $y^2=76x^6+108x^5+52x^4+124x^3+15x^2+86x+147$
• $y^2=169x^6+79x^5+58x^4+124x^2+50x+68$
• $y^2=170x^6+112x^5+20x^4+159x^3+83x^2+38x+139$
• $y^2=87x^6+106x^5+37x^4+116x^3+157x^2+119x+1$
• $y^2=65x^6+15x^5+10x^4+94x^3+135x^2+137x+101$
• $y^2=143x^6+170x^5+76x^4+128x^3+107x^2+53x+162$
• $y^2=100x^6+83x^5+22x^4+108x^3+142x^2+4x+2$
• $y^2=53x^6+72x^5+24x^4+111x^3+73x^2+84x+11$
• $y^2=96x^6+5x^5+81x^4+26x^3+152x^2+52x+94$
• $y^2=116x^6+115x^5+127x^4+159x^3+79x^2+104x+138$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is 4.0.1007325.1.

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.bt_bgm	$2$	(not in LMFDB)