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

• Label: 2.173.abx_bki
• 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:	$( 1 - 26 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$
	$1 - 49 x + 944 x^{2} - 8477 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0485897903475$, $\pm0.161302001611$
Angle rank:	$2$ (numerical)
Jacobians:	$3$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22348$	$880511200$	$26786438306368$	$802338869747056000$	$24013819842264500046748$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$125$	$29417$	$5173406$	$895722369$	$154963969465$	$26808757327334$	$4637914386034957$	$802359178958629921$	$138808137875313401558$	$24013807852489475491457$

Jacobians and polarizations

This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=58x^6+46x^5+121x^4+23x^3+38x^2+18x+88$
• $y^2=103x^6+130x^5+26x^4+33x^3+24x^2+58x+75$
• $y^2=90x^6+108x^5+136x^4+35x^3+150x^2+5x+128$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{173}$

The isogeny class factors as 1.173.aba $\times$ 1.173.ax 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.aba : \(\Q(\sqrt{-1}) \).
• 1.173.ax : \(\Q(\sqrt{-163}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.173.ad_ajs	$2$	(not in LMFDB)
2.173.d_ajs	$2$	(not in LMFDB)
2.173.bx_bki	$2$	(not in LMFDB)