Abelian variety isogeny class 2.167.abt_bga over $\F_{167}$

• Label: 2.167.abt_bga
• Base field: $\F_{167}$
• 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:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 832 x^{2} - 7515 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0610178644081$, $\pm0.225483190516$
Angle rank:	$2$ (numerical)
Number field:	4.0.7466184.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21162$	$767799684$	$21685675105944$	$604977214511340576$	$16871960336211560539182$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$123$	$27529$	$4656114$	$777809305$	$129892235133$	$21691961945818$	$3622557529931379$	$604967115633690769$	$101029508515584646398$	$16871927924836345521889$

Jacobians and polarizations

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

• $y^2=43x^6+19x^5+81x^4+36x^3+x^2+82x+65$
• $y^2=164x^6+130x^5+12x^4+64x^3+154x^2+19x+125$
• $y^2=27x^6+52x^5+128x^4+51x^3+71x^2+157x+135$
• $y^2=161x^6+142x^5+41x^4+81x^3+86x^2+37x+100$
• $y^2=52x^6+121x^5+132x^4+119x^3+7x^2+108x+123$
• $y^2=66x^6+88x^5+26x^4+38x^3+89x^2+77x+8$
• $y^2=102x^6+134x^5+119x^4+57x^3+155x^2+139x+19$
• $y^2=46x^6+5x^5+110x^4+117x^3+112x^2+155x+68$
• $y^2=129x^6+68x^5+37x^4+149x^3+154x^2+27x+79$
• $y^2=12x^6+7x^5+162x^4+18x^3+142x^2+49x+159$
• $y^2=141x^6+159x^5+23x^4+76x^3+76x^2+134x+145$
• $y^2=111x^6+116x^5+164x^4+4x^3+131x^2+57x+49$
• $y^2=165x^6+66x^5+160x^4+114x^3+121x^2+14x+146$
• $y^2=121x^6+131x^5+22x^4+42x^3+138x^2+28x+38$
• $y^2=49x^6+4x^5+125x^4+110x^3+90x^2+144x+39$
• $y^2=60x^6+118x^5+15x^4+94x^3+103x^2+94x+108$
• $y^2=140x^6+68x^5+79x^4+25x^3+24x^2+125x+4$
• $y^2=28x^6+56x^5+81x^4+121x^3+86x^2+141x+70$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$

The endomorphism algebra of this simple isogeny class is 4.0.7466184.2.

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
2.167.bt_bga	$2$	(not in LMFDB)