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

• Label: 2.173.abu_bho
• 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:	$1 - 46 x + 872 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.110664567545$, $\pm0.200287313354$
Angle rank:	$2$ (numerical)
Number field:	4.0.2772288.1
Galois group:	$D_{4}$
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22798$	$884699188$	$26804235111838$	$802393063990308304$	$24013950198826443390238$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$128$	$29558$	$5176844$	$895782870$	$154964810668$	$26808766778774$	$4637914471195504$	$802359179586669790$	$138808137880750303376$	$24013807852593727958438$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=68x^6+70x^5+109x^4+54x^3+29x^2+101x+115$
• $y^2=94x^6+44x^5+10x^4+144x^3+17x^2+118x+87$
• $y^2=51x^6+7x^5+123x^4+102x^3+106x^2+57x+123$
• $y^2=7x^6+134x^5+68x^4+51x^3+15x^2+10x+76$
• $y^2=17x^6+69x^5+55x^4+61x^3+82x^2+134x+129$
• $y^2=7x^6+104x^5+9x^4+159x^3+23x^2+70x+79$
• $y^2=59x^6+113x^4+116x^3+56x^2+59x+161$
• $y^2=20x^6+73x^5+52x^4+60x^3+84x^2+79x+46$
• $y^2=47x^6+114x^5+50x^4+77x^3+40x^2+33x+140$
• $y^2=76x^6+141x^5+88x^4+111x^3+163x^2+157x+172$
• $y^2=171x^6+109x^5+141x^4+39x^3+107x^2+151x+150$
• $y^2=90x^6+102x^5+14x^4+55x^3+34x^2+23x+128$
• $y^2=115x^6+23x^5+151x^4+67x^3+128x^2+66x+115$
• $y^2=17x^6+105x^5+108x^4+127x^3+55x^2+4x+3$
• $y^2=8x^6+142x^5+60x^4+72x^3+19x^2+80x+138$
• $y^2=120x^6+43x^5+132x^4+127x^3+93x^2+38x+39$
• $y^2=5x^6+63x^5+24x^4+82x^3+78x^2+163x+138$
• $y^2=53x^6+73x^5+137x^4+49x^3+35x^2+87x+104$

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 4.0.2772288.1.

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.bu_bho	$2$	(not in LMFDB)