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

• Label: 2.173.abs_bfg
• 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:	$1 - 44 x + 812 x^{2} - 7612 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0220781886823$, $\pm0.264129150942$
Angle rank:	$2$ (numerical)
Number field:	4.0.80128.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$23086$	$886456228$	$26804419010782$	$802360384340108944$	$24013758275941299367726$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$130$	$29618$	$5176882$	$895746390$	$154963572170$	$26808741135074$	$4637914084842602$	$802359175273675870$	$138808137848375227042$	$24013807852505728010738$

Jacobians and polarizations

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

• $y^2=38x^6+54x^5+90x^4+20x^3+106x^2+44x+159$
• $y^2=37x^6+59x^5+122x^4+154x^3+32x^2+144x+73$
• $y^2=156x^6+46x^5+90x^4+163x^3+39x^2+102x+114$
• $y^2=2x^6+106x^5+40x^4+103x^3+26x^2+37x+145$
• $y^2=108x^6+133x^5+126x^4+121x^3+83x^2+134x+153$
• $y^2=96x^6+73x^5+39x^4+105x^3+42x^2+58x+77$
• $y^2=99x^6+151x^5+151x^4+x^3+59x^2+102x+54$
• $y^2=133x^6+51x^5+117x^4+171x^3+31x^2+29x+108$
• $y^2=138x^6+72x^5+97x^4+129x^3+146x^2+21x+64$
• $y^2=35x^6+9x^5+141x^4+51x^3+62x^2+60x+99$
• $y^2=104x^6+31x^5+48x^4+112x^3+52x^2+52x+111$
• $y^2=106x^6+162x^5+66x^4+80x^3+104x^2+78x+114$
• $y^2=49x^6+75x^5+16x^4+156x^3+68x^2+43x+73$
• $y^2=80x^6+49x^5+72x^4+132x^3+89x^2+166x+91$
• $y^2=127x^6+9x^5+22x^4+25x^3+103x^2+79x+91$
• $y^2=47x^6+112x^5+112x^4+93x^3+142x^2+145x+94$
• $y^2=79x^6+120x^5+164x^4+89x^3+4x^2+71x+49$
• $y^2=59x^6+140x^5+122x^3+19x^2+50x+103$

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 4.0.80128.1.

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.bs_bfg	$2$	(not in LMFDB)