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

• Label: 2.173.abt_bgr
• 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:	$1 - 45 x + 849 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.125022143764$, $\pm0.211741254026$
Angle rank:	$2$ (numerical)
Number field:	4.0.4516525.1
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22949$	$886037941$	$26809459414481$	$802406734477000501$	$24013974516820204176464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$129$	$29603$	$5177853$	$895798131$	$154964967594$	$26808767494787$	$4637914459930713$	$802359179242397923$	$138808137875591659869$	$24013807852540865988278$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=140x^6+4x^5+170x^4+115x^3+78x^2+133x+126$
• $y^2=105x^6+116x^5+56x^4+105x^3+163x^2+27x+115$
• $y^2=106x^6+111x^5+93x^4+83x^3+52x^2+156x+161$
• $y^2=101x^6+133x^5+65x^4+55x^3+22x^2+67x+14$
• $y^2=124x^6+133x^5+121x^4+74x^3+158x^2+85x+170$
• $y^2=104x^6+116x^5+x^4+91x^3+170x^2+131x+107$
• $y^2=91x^6+142x^5+142x^4+124x^3+77x^2+51x+103$
• $y^2=43x^6+72x^5+118x^4+38x^3+51x^2+87x+43$
• $y^2=102x^5+163x^4+3x^3+134x^2+48x+88$
• $y^2=59x^6+127x^5+154x^4+40x^3+80x^2+80x+131$
• $y^2=143x^6+108x^5+78x^4+13x^3+10x^2+90x+74$
• $y^2=127x^6+2x^5+91x^4+103x^3+141x^2+41x+105$

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 4.0.4516525.1.

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.bt_bgr	$2$	(not in LMFDB)