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

• Label: 2.163.abr_bds
• 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:	$1 - 43 x + 772 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.00500927175908$, $\pm0.260180428357$
Angle rank:	$2$ (numerical)
Number field:	4.0.236600.1
Galois group:	$D_{4}$
Jacobians:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20290$	$697854260$	$18751268000440$	$498311180689949600$	$13239603851228302684750$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$26265$	$4329802$	$705911433$	$115063337931$	$18755359303170$	$3057125037700897$	$498311411551609233$	$81224760507406380046$	$13239635966863229242825$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=101x^6+73x^5+18x^4+124x^3+157x^2+46x+18$
• $y^2=34x^6+51x^5+100x^4+106x^3+141x^2+155x+154$

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 4.0.236600.1.

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_bds	$2$	(not in LMFDB)