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

• Label: 2.167.abw_bja
• 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:	$( 1 - 24 x + 167 x^{2} )^{2}$
	$1 - 48 x + 910 x^{2} - 8016 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.121023609245$, $\pm0.121023609245$
Angle rank:	$1$ (numerical)
Jacobians:	$33$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20736$	$764411904$	$21675207280896$	$604962784643383296$	$16871988646109807790336$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$120$	$27406$	$4653864$	$777790750$	$129892453080$	$21691973746222$	$3622557800122248$	$604967120056796734$	$101029508571146152248$	$16871927925339398065486$

Jacobians and polarizations

This isogeny class contains the Jacobians of 33 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=128x^6+165x^5+34x^4+126x^3+34x^2+165x+128$
• $y^2=100x^6+9x^4+9x^2+100$
• $y^2=74x^6+29x^5+128x^4+24x^3+128x^2+29x+74$
• $y^2=153x^6+110x^4+110x^2+153$
• $y^2=74x^6+139x^5+36x^4+54x^3+128x^2+46x+82$
• $y^2=100x^6+81x^5+6x^4+25x^3+72x^2+141x+122$
• $y^2=162x^6+110x^5+145x^4+165x^3+145x^2+110x+162$
• $y^2=12x^6+136x^5+112x^4+158x^3+112x^2+136x+12$
• $y^2=69x^6+149x^5+12x^4+149x^3+152x^2+118x+134$
• $y^2=15x^6+152x^5+78x^4+114x^3+39x^2+38x+148$
• $y^2=60x^6+166x^5+101x^4+109x^3+131x^2+146x+80$
• $y^2=66x^6+12x^4+12x^2+66$
• $y^2=110x^6+77x^5+133x^4+129x^3+100x^2+157x+35$
• $y^2=126x^6+44x^5+84x^4+73x^3+124x^2+108x+77$
• $y^2=89x^6+122x^5+112x^4+63x^3+150x^2+89x+141$
• $y^2=80x^6+63x^5+18x^4+12x^3+147x^2+152x+30$
• $y^2=27x^6+76x^5+141x^4+124x^3+85x^2+84x+38$
• $y^2=25x^6+50x^4+50x^2+25$
• $y^2=58x^6+105x^5+x^4+16x^3+152x^2+78x+141$
• $y^2=114x^6+161x^5+147x^4+152x^3+29x^2+45x+29$
• and

• $y^2=143x^6+148x^5+62x^4+2x^3+62x^2+148x+143$
• $y^2=120x^6+86x^5+82x^4+7x^3+82x^2+86x+120$
• $y^2=166x^6+145x^5+159x^4+31x^3+165x^2+103x+60$
• $y^2=158x^6+157x^5+79x^4+84x^3+79x^2+157x+158$
• $y^2=136x^6+65x^5+141x^4+135x^3+9x^2+11x+95$
• $y^2=91x^6+89x^5+152x^4+40x^3+152x^2+89x+91$
• $y^2=159x^6+x^5+49x^4+22x^3+49x^2+x+159$
• $y^2=139x^6+56x^5+118x^4+34x^3+138x^2+61x+45$
• $y^2=123x^6+61x^4+61x^2+123$
• $y^2=55x^6+165x^5+125x^4+155x^3+125x^2+165x+55$
• $y^2=33x^6+91x^5+100x^4+63x^3+100x^2+91x+33$
• $y^2=76x^6+141x^5+81x^4+85x^3+81x^2+141x+76$
• $y^2=5x^6+150x^4+150x^2+5$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{167}$

The isogeny class factors as 1.167.ay^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-23}) \)$)$

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_aji	$2$	(not in LMFDB)
2.167.bw_bja	$2$	(not in LMFDB)
2.167.y_pt	$3$	(not in LMFDB)