Abelian variety isogeny class 2.163.abr_beb over $\F_{163}$

• Label: 2.163.abr_beb
• Base field: $\F_{163}$
• 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:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$1 - 43 x + 781 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.103645999267$, $\pm0.236451097903$
Angle rank:	$2$ (numerical)
Number field:	4.0.16736741.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20299$	$698346497$	$18756303423949$	$498338438000287469$	$13239706046996518355824$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$26283$	$4330963$	$705950043$	$115064226096$	$18755375002023$	$3057125261377609$	$498311414200696611$	$81224760534892861159$	$13239635967151756544518$

Jacobians and polarizations

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

• $y^2=73x^6+101x^5+38x^4+49x^3+39x^2+41x+15$
• $y^2=100x^6+123x^5+102x^4+142x^3+45x^2+82x+94$
• $y^2=18x^6+67x^5+6x^4+2x^3+29x^2+39x+43$
• $y^2=94x^6+67x^5+55x^4+118x^3+118x^2+111x+141$
• $y^2=42x^6+64x^5+4x^4+100x^3+40x^2+106x+94$
• $y^2=80x^6+73x^5+27x^4+29x^3+x^2+7x+94$
• $y^2=62x^6+154x^5+147x^4+144x^3+161x^2+57x+113$
• $y^2=78x^6+103x^5+161x^4+15x^3+16x^2+92x+122$
• $y^2=140x^6+96x^5+44x^4+56x^3+131x^2+134x+86$
• $y^2=94x^6+139x^5+70x^4+6x^3+86x^2+40x+74$
• $y^2=45x^6+46x^5+56x^4+9x^3+15x^2+99x+82$
• $y^2=29x^6+62x^5+109x^4+100x^3+45x^2+150x+80$
• $y^2=78x^6+137x^5+157x^4+39x^3+114x^2+118x+37$
• $y^2=161x^6+23x^5+82x^4+90x^3+69x^2+120x+19$
• $y^2=112x^6+135x^5+87x^4+149x^3+46x^2+113x+62$
• $y^2=148x^6+123x^5+59x^4+24x^3+118x^2+155x+149$
• $y^2=146x^6+78x^5+8x^4+158x^3+8x^2+x+116$
• $y^2=112x^6+31x^5+32x^4+107x^3+149x^2+160x+103$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The endomorphism algebra of this simple isogeny class is 4.0.16736741.1.

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
2.163.br_beb	$2$	(not in LMFDB)