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

• Label: 2.173.abv_bin
• 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:	$1 - 47 x + 897 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.114645392612$, $\pm0.176096830998$
Angle rank:	$2$ (numerical)
Number field:	4.0.410525.1
Galois group:	$D_{4}$
Jacobians:	$19$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22649$	$883424245$	$26799758770301$	$802384333405685525$	$24013949178262395007744$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$127$	$29515$	$5175979$	$895773123$	$154964804082$	$26808769287595$	$4637914538680039$	$802359180713688003$	$138808137893601119227$	$24013807852662073936950$

Jacobians and polarizations

This isogeny class contains the Jacobians of 19 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=35x^6+52x^5+127x^4+13x^3+100x^2+99x+138$
• $y^2=132x^6+2x^5+94x^4+85x^3+32x^2+102x+13$
• $y^2=59x^6+26x^5+125x^4+151x^3+21x^2+155x+159$
• $y^2=64x^6+69x^5+58x^4+124x^3+11x^2+34x+36$
• $y^2=66x^6+169x^5+20x^4+47x^3+24x^2+83x+19$
• $y^2=6x^6+6x^5+151x^4+38x^3+159x^2+83x+65$
• $y^2=137x^6+76x^5+47x^4+6x^3+59x^2+17x+166$
• $y^2=43x^5+8x^4+113x^3+167x^2+66x+135$
• $y^2=21x^6+150x^5+7x^4+86x^3+124x^2+26x+29$
• $y^2=69x^6+2x^5+107x^4+144x^3+45x^2+157x+58$
• $y^2=145x^6+140x^5+135x^4+14x^3+120x^2+96x+86$
• $y^2=85x^6+65x^5+62x^4+147x^3+72x^2+146x+123$
• $y^2=127x^6+89x^5+161x^4+90x^3+154x^2+112x+123$
• $y^2=38x^6+116x^5+9x^4+114x^3+141x^2+92x+155$
• $y^2=104x^6+59x^5+124x^4+141x^3+12x^2+164x+142$
• $y^2=105x^6+44x^5+45x^4+99x^3+36x^2+5x+134$
• $y^2=83x^5+172x^4+67x^3+61x^2+3x+32$
• $y^2=153x^6+158x^5+120x^4+80x^3+108x^2+130x+134$
• $y^2=123x^6+7x^5+166x^4+166x^3+144x^2+x+51$

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 4.0.410525.1.

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.bv_bin	$2$	(not in LMFDB)