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

• Label: 2.167.abs_bfm
• Base field: $\F_{167}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$( 1 - 22 x + 167 x^{2} )^{2}$
	$1 - 44 x + 818 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.175872025744$, $\pm0.175872025744$
Angle rank:	$1$ (numerical)
Jacobians:	$34$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21316$	$769507600$	$21695454834244$	$605018886636160000$	$16872101892051917530756$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$124$	$27590$	$4658212$	$777862878$	$129893324924$	$21691979946470$	$3622557766630052$	$604967117857469758$	$101029508522162832124$	$16871927924551779426950$

Jacobians and polarizations

This isogeny class contains the Jacobians of 34 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=73x^6+110x^5+130x^4+57x^3+154x^2+61x+13$
• $y^2=129x^6+91x^5+89x^4+34x^3+46x^2+68x+14$
• $y^2=10x^6+95x^5+18x^4+53x^3+37x^2+122x+72$
• $y^2=129x^6+129x^5+140x^4+106x^3+140x^2+129x+129$
• $y^2=2x^6+124x^5+159x^4+25x^3+6x^2+3x+26$
• $y^2=62x^6+23x^5+108x^4+146x^3+108x^2+23x+62$
• $y^2=115x^6+80x^5+126x^4+121x^3+14x^2+135x+32$
• $y^2=40x^6+60x^5+135x^4+99x^3+156x^2+36x+136$
• $y^2=37x^6+77x^5+17x^4+103x^3+102x^2+82x+75$
• $y^2=148x^6+59x^5+124x^4+43x^3+136x^2+126x+118$
• $y^2=126x^6+68x^5+145x^4+87x^3+40x^2+113x+31$
• $y^2=8x^6+94x^5+100x^4+148x^3+137x^2+133x+139$
• $y^2=60x^6+144x^5+140x^4+102x^3+140x^2+144x+60$
• $y^2=150x^6+155x^5+103x^4+12x^3+4x^2+63x+78$
• $y^2=142x^6+131x^5+67x^4+82x^3+53x^2+101x+142$
• $y^2=71x^6+155x^5+71x^4+49x^3+41x^2+55x+160$
• $y^2=71x^6+26x^5+126x^4+55x^3+53x^2+x+72$
• $y^2=17x^6+110x^5+154x^4+7x^3+132x^2+37x+104$
• $y^2=37x^6+24x^5+45x^4+53x^3+26x^2+33x+73$
• $y^2=63x^6+4x^5+114x^4+127x^3+4x^2+9x+150$
• and

• $y^2=80x^6+28x^5+31x^4+41x^3+29x^2+34x+33$
• $y^2=155x^6+85x^5+107x^4+59x^3+2x^2+33x+166$
• $y^2=43x^6+137x^5+128x^4+163x^3+153x^2+7x+36$
• $y^2=153x^6+144x^5+133x^4+78x^3+87x^2+57x+59$
• $y^2=79x^6+93x^5+139x^4+139x^3+139x^2+93x+79$
• $y^2=57x^6+89x^4+89x^2+57$
• $y^2=65x^6+105x^5+163x^4+104x^3+2x^2+15x+142$
• $y^2=81x^6+43x^5+14x^4+117x^3+2x^2+35x+74$
• $y^2=64x^6+120x^5+42x^4+80x^3+58x^2+44x+86$
• $y^2=78x^6+132x^5+52x^4+44x^3+160x^2+81x+110$
• $y^2=138x^6+52x^5+53x^4+91x^3+118x^2+59x+24$
• $y^2=43x^6+67x^5+148x^4+83x^3+148x^2+67x+43$
• $y^2=153x^6+78x^4+78x^2+153$
• $y^2=51x^6+47x^5+69x^4+64x^3+69x^2+47x+51$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{167}$

The isogeny class factors as 1.167.aw^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-46}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.167.a_afu	$2$	(not in LMFDB)
2.167.bs_bfm	$2$	(not in LMFDB)
2.167.w_mf	$3$	(not in LMFDB)