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

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

Invariants

Base field:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$
	$1 - 47 x + 896 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.100717649571$, $\pm0.184705758688$
Angle rank:	$2$ (numerical)
Jacobians:	$12$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22648$	$883362592$	$26799027537184$	$802379630288677504$	$24013927728810561231448$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$127$	$29513$	$5175838$	$895767873$	$154964665667$	$26808766427558$	$4637914490722367$	$802359180069900961$	$138808137887413092694$	$24013807852645961692193$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=2x^6+110x^5+126x^4+124x^3+137x^2+64x+136$
• $y^2=164x^6+20x^5+121x^4+150x^3+74x^2+134x+31$
• $y^2=83x^6+79x^5+109x^4+75x^3+106x^2+40x+32$
• $y^2=142x^6+74x^5+140x^4+32x^3+4x^2+25x+129$
• $y^2=11x^6+61x^5+42x^4+139x^3+99x^2+156x+99$
• $y^2=48x^6+2x^5+170x^4+20x^3+76x^2+109x+63$
• $y^2=20x^6+101x^5+31x^4+153x^3+66x^2+166x+42$
• $y^2=89x^6+76x^5+5x^4+165x^3+115x^2+40x+152$
• $y^2=159x^6+135x^5+47x^4+127x^3+78x^2+25x+156$
• $y^2=129x^6+110x^5+148x^4+114x^3+155x^2+81x+139$
• $y^2=83x^6+5x^5+69x^4+74x^3+86x^2+163x+129$
• $y^2=156x^6+86x^5+96x^4+27x^3+95x^2+172x+112$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{173}$

The isogeny class factors as 1.173.az $\times$ 1.173.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.173.az : \(\Q(\sqrt{-67}) \).
• 1.173.aw : \(\Q(\sqrt{-13}) \).

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.ad_ahw	$2$	(not in LMFDB)
2.173.d_ahw	$2$	(not in LMFDB)
2.173.bv_bim	$2$	(not in LMFDB)