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

• Label: 2.173.abx_bkj
• 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:	$1 - 49 x + 945 x^{2} - 8477 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0729523342082$, $\pm0.151505752657$
Angle rank:	$2$ (numerical)
Number field:	4.0.129725.1
Galois group:	$D_{4}$
Jacobians:	$5$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22349$	$880572949$	$26787200771249$	$802344088938125141$	$24013845849262471846864$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$125$	$29419$	$5173553$	$895728195$	$154964137290$	$26808761254123$	$4637914464763061$	$802359180349782339$	$138808137897286784129$	$24013807852800902933814$

Jacobians and polarizations

This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=102x^6+137x^5+64x^4+44x^3+164x^2+61x+168$
• $y^2=160x^6+125x^5+54x^4+164x^3+156x^2+127x+86$
• $y^2=108x^6+164x^5+6x^4+164x^3+158x^2+111x+65$
• $y^2=110x^6+124x^5+131x^4+90x^3+42x^2+118x+46$
• $y^2=113x^6+153x^5+138x^4+83x^3+161x^2+43x+52$

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 4.0.129725.1.

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.bx_bkj	$2$	(not in LMFDB)