Abelian variety isogeny class 2.199.abz_boh over $\F_{199}$

• Label: 2.199.abz_boh
• Base field: $\F_{199}$
• 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:	$\F_{199}$
Dimension:	$2$
L-polynomial:	$1 - 51 x + 1047 x^{2} - 10149 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.107558551199$, $\pm0.167827717537$
Angle rank:	$2$ (numerical)
Number field:	4.0.440725.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30449$	$1548301201$	$62080947273431$	$2459410854718312429$	$97394023757570826483824$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$149$	$39095$	$7877693$	$1568262579$	$312080710964$	$62103863305811$	$12358664627459831$	$2459374195881372019$	$489415464161640788987$	$97393677359970102360350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=179x^6+8x^5+11x^4+173x^3+163x^2+76x+198$
• $y^2=168x^6+147x^5+161x^4+35x^3+141x^2+34x+129$
• $y^2=82x^6+30x^5+151x^4+121x^3+165x^2+43x+75$
• $y^2=94x^6+87x^5+34x^4+48x^3+157x^2+63x+168$
• $y^2=155x^6+124x^5+73x^4+19x^3+24x^2+108x+86$
• $y^2=78x^6+127x^5+51x^4+134x^3+141x^2+135x+111$
• $y^2=129x^6+122x^5+44x^4+94x^3+174x^2+106x+149$
• $y^2=187x^6+99x^5+43x^4+136x^3+114x^2+167x+185$
• $y^2=83x^6+7x^5+110x^4+91x^3+18x^2+27x+179$
• $y^2=34x^6+42x^5+54x^4+6x^3+46x^2+115x+59$
• $y^2=74x^6+192x^5+106x^4+162x^3+149x^2+160x+13$
• $y^2=52x^6+188x^5+121x^4+91x^3+169x^2+120x+80$
• $y^2=37x^6+65x^5+15x^4+97x^3+135x^2+177x+196$
• $y^2=74x^6+188x^5+159x^4+163x^3+62x^2+113x+118$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{199}$.

Endomorphism algebra over $\F_{199}$

The endomorphism algebra of this simple isogeny class is 4.0.440725.1.

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
2.199.bz_boh	$2$	(not in LMFDB)