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

• Label: 2.167.abt_bgd
• Base field: $\F_{167}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 45 x + 835 x^{2} - 7515 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0912353233239$, $\pm0.214251472967$
Angle rank:	$2$ (numerical)
Number field:	4.0.6112701.2
Galois group:	$D_{4}$
Jacobians:	$60$

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21165$	$767972025$	$21687564336795$	$604988336424448125$	$16872006366889461193200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$123$	$27535$	$4656519$	$777823603$	$129892589508$	$21691968791155$	$3622557637474269$	$604967117020587283$	$101029508529926206293$	$16871927924944914675550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 60 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=117x^6+47x^5+151x^4+37x^3+48x^2+155x+36$
• $y^2=157x^6+46x^5+46x^4+152x^3+6x^2+110x+140$
• $y^2=35x^6+117x^5+112x^4+96x^3+16x^2+145x+109$
• $y^2=41x^6+90x^5+137x^4+146x^3+103x^2+85x+18$
• $y^2=86x^6+30x^5+116x^4+143x^3+122x^2+84x+23$
• $y^2=13x^6+128x^5+25x^4+87x^3+129x^2+17x+125$
• $y^2=45x^6+139x^5+43x^4+35x^3+52x^2+149x+41$
• $y^2=5x^6+15x^5+63x^4+22x^3+154x^2+148x+80$
• $y^2=120x^6+25x^5+59x^4+53x^3+149x^2+120x+21$
• $y^2=159x^6+113x^5+143x^4+7x^3+102x^2+17x+137$
• $y^2=75x^6+6x^5+108x^4+96x^3+59x^2+127x+109$
• $y^2=101x^6+107x^5+89x^4+57x^3+147x^2+35x+104$
• $y^2=33x^6+130x^5+61x^4+114x^3+79x^2+76x+34$
• $y^2=166x^6+72x^5+47x^4+113x^3+80x^2+51x+132$
• $y^2=56x^6+148x^5+47x^4+126x^3+101x^2+95x+18$
• $y^2=61x^6+114x^5+165x^4+151x^3+22x^2+66x+143$
• $y^2=152x^6+32x^5+152x^4+72x^3+67x^2+53x+151$
• $y^2=30x^6+138x^5+155x^4+41x^3+107x^2+133x+138$
• $y^2=114x^6+40x^5+163x^4+128x^3+87x^2+14x+8$
• $y^2=16x^6+128x^5+90x^4+71x^3+129x^2+123x+62$
• and

• $y^2=90x^6+61x^5+140x^4+135x^3+51x^2+101x+46$
• $y^2=52x^6+75x^5+158x^4+10x^3+2x^2+78x+138$
• $y^2=144x^6+99x^5+20x^4+154x^3+150x^2+4x+2$
• $y^2=156x^6+74x^5+6x^4+19x^3+92x^2+91x+14$
• $y^2=91x^6+21x^5+59x^4+71x^3+105x^2+101x+67$
• $y^2=123x^6+144x^5+30x^4+155x^3+34x^2+46x+75$
• $y^2=46x^6+164x^5+83x^4+49x^3+84x^2+29x+61$
• $y^2=35x^6+92x^5+16x^4+147x^3+104x^2+89x+12$
• $y^2=65x^6+140x^5+68x^4+35x^3+27x^2+35x+95$
• $y^2=134x^6+76x^5+137x^4+31x^3+113x^2+44x+143$
• $y^2=161x^6+122x^5+x^4+94x^3+x^2+42x+58$
• $y^2=55x^6+22x^5+30x^4+78x^3+147x^2+67x+80$
• $y^2=126x^6+52x^5+95x^4+102x^3+78x^2+10x+61$
• $y^2=126x^6+122x^5+59x^4+6x^3+96x^2+97x+137$
• $y^2=102x^6+107x^5+158x^4+110x^3+x^2+63x+97$
• $y^2=118x^6+111x^5+111x^4+63x^3+63x^2+133x+104$
• $y^2=5x^6+142x^5+31x^4+73x^3+47x^2+87x+23$
• $y^2=31x^6+91x^5+37x^4+148x^3+132x^2+3x+26$
• $y^2=92x^6+159x^5+151x^4+31x^3+153x^2+97x+164$
• $y^2=89x^6+59x^5+115x^4+140x^3+4x^2+79x+6$
• $y^2=107x^6+155x^5+128x^4+46x^3+40x^2+91x+83$
• $y^2=142x^6+74x^5+53x^4+25x^3+97x^2+115x+86$
• $y^2=139x^5+68x^4+109x^3+25x^2+110x+129$
• $y^2=86x^6+70x^5+79x^4+103x^3+84x^2+19x+119$
• $y^2=93x^6+54x^5+119x^4+58x^3+78x^2+149x+5$
• $y^2=74x^6+155x^5+158x^4+38x^3+156x^2+95x+110$
• $y^2=33x^6+109x^5+103x^4+27x^3+112x^2+4x+117$
• $y^2=24x^6+136x^5+41x^4+23x^3+109x^2+81x+81$
• $y^2=92x^6+21x^5+150x^4+63x^3+137x^2+106x+166$
• $y^2=106x^6+6x^5+83x^4+77x^3+81x^2+57x+111$
• $y^2=67x^6+63x^5+57x^4+27x^3+44x^2+25x+130$
• $y^2=166x^6+27x^5+153x^4+17x^3+139x^2+143x+36$
• $y^2=68x^6+64x^5+62x^4+31x^3+93x^2+65x+3$
• $y^2=145x^6+132x^5+84x^4+9x^3+165x^2+22x+45$
• $y^2=150x^6+108x^5+17x^4+54x^3+46x^2+94x+68$
• $y^2=10x^6+31x^5+8x^4+19x^3+80x^2+60x+135$
• $y^2=53x^6+45x^5+9x^4+146x^3+98x^2+126x+110$
• $y^2=137x^6+110x^5+56x^4+72x^3+67x^2+148x+147$
• $y^2=25x^6+66x^5+67x^4+58x^3+80x^2+112x+45$
• $y^2=52x^6+84x^5+97x^4+46x^3+16x^2+18x+142$

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 4.0.6112701.2.

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_bgd	$2$	(not in LMFDB)