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

• Label: 2.173.abs_bfh
• 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:	$1 - 44 x + 813 x^{2} - 7612 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0375459716603$, $\pm0.262163108058$
Angle rank:	$2$ (numerical)
Number field:	4.0.1031441.3
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$23087$	$886517713$	$26805103355456$	$802364410055806169$	$24013774776519431260207$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$130$	$29620$	$5177014$	$895750884$	$154963678650$	$26808743110150$	$4637914115755330$	$802359175716320964$	$138808137854808610702$	$24013807852608324482100$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=71x^6+20x^5+5x^4+4x^3+97x^2+166x+119$
• $y^2=2x^6+172x^5+74x^4+81x^3+21x^2+24x+123$
• $y^2=87x^6+41x^5+134x^4+11x^3+56x^2+x+80$
• $y^2=37x^6+52x^5+166x^4+140x^3+74x^2+135x+10$
• $y^2=7x^6+113x^5+104x^4+170x^3+144x^2+79x+29$
• $y^2=16x^6+70x^5+21x^4+85x^3+75x^2+112x+27$
• $y^2=115x^6+162x^5+92x^4+85x^3+109x^2+120x+130$
• $y^2=85x^6+157x^5+137x^4+166x^3+35x^2+103x+154$
• $y^2=8x^6+73x^5+36x^4+160x^3+144x^2+40x+139$
• $y^2=19x^6+138x^5+98x^4+8x^3+136x^2+41x+27$
• $y^2=25x^6+82x^5+170x^4+25x^3+146x^2+8x+157$
• $y^2=161x^6+100x^5+103x^4+153x^3+114x^2+92x+109$
• $y^2=69x^6+12x^5+90x^4+21x^3+40x^2+42x+53$
• $y^2=46x^6+39x^5+100x^4+96x^3+65x^2+113x+36$
• $y^2=43x^6+7x^5+8x^4+27x^3+154x^2+76x+69$
• $y^2=99x^6+113x^5+36x^4+157x^3+138x^2+118x+105$
• $y^2=48x^6+148x^5+22x^4+99x^3+83x^2+48x+37$
• $y^2=147x^6+67x^5+15x^4+142x^3+140x^2+149x+8$
• $y^2=28x^6+38x^5+73x^4+145x^3+9x^2+58x+66$
• $y^2=105x^6+85x^5+31x^4+19x^3+156x^2+123x+61$
• $y^2=171x^6+78x^5+59x^4+109x^3+136x^2+83x+48$
• $y^2=96x^6+117x^5+97x^4+62x^3+147x^2+2x+72$
• $y^2=147x^6+98x^5+133x^4+42x^3+80x^2+47x+41$
• $y^2=127x^6+49x^5+148x^4+97x^3+4x^2+63x+127$

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 4.0.1031441.3.

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_bfh	$2$	(not in LMFDB)