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

• Label: 2.167.abs_bfl
• 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:	$( 1 - 23 x + 167 x^{2} )( 1 - 21 x + 167 x^{2} )$
	$1 - 44 x + 817 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.150776270497$, $\pm0.198098183086$
Angle rank:	$2$ (numerical)
Jacobians:	$45$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21315$	$769450185$	$21694839097680$	$605015406454962825$	$16872088518296313993075$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$124$	$27588$	$4658080$	$777858404$	$129893221964$	$21691978223886$	$3622557747100388$	$604967117792091076$	$101029508525635846240$	$16871927924663439940068$

Jacobians and polarizations

This isogeny class contains the Jacobians of 45 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=2x^6+134x^5+3x^4+83x^3+114x^2+110x+25$
• $y^2=130x^6+134x^5+64x^4+36x^3+75x^2+166x+81$
• $y^2=29x^6+19x^5+85x^4+104x^3+12x^2+47x+152$
• $y^2=86x^6+166x^5+86x^4+15x^3+149x^2+35x+129$
• $y^2=127x^6+64x^5+23x^4+44x^3+41x^2+49x+28$
• $y^2=159x^6+2x^5+52x^4+19x^3+45x^2+137x+91$
• $y^2=29x^6+72x^5+97x^4+8x^3+66x^2+88x+97$
• $y^2=140x^6+84x^5+36x^4+83x^3+126x^2+27x+74$
• $y^2=6x^6+43x^5+40x^4+137x^3+70x^2+163x+100$
• $y^2=22x^6+119x^5+17x^4+56x^3+165x^2+149x+112$
• $y^2=24x^6+93x^5+50x^4+26x^3+6x^2+132x+14$
• $y^2=107x^6+124x^5+132x^4+133x^3+x^2+38x+29$
• $y^2=121x^6+153x^5+44x^4+79x^3+97x^2+164x+84$
• $y^2=16x^6+22x^5+133x^4+23x^3+47x^2+77x+11$
• $y^2=91x^6+145x^5+161x^4+95x^3+135x^2+135x+43$
• $y^2=80x^6+142x^5+156x^4+131x^3+70x^2+129x+46$
• $y^2=150x^6+47x^5+136x^4+120x^3+146x^2+81x+124$
• $y^2=117x^6+28x^5+84x^4+105x^3+65x^2+89x+95$
• $y^2=113x^6+5x^5+45x^4+33x^3+71x^2+71x+46$
• $y^2=60x^6+160x^5+136x^4+156x^3+104x^2+30x+70$
• and

• $y^2=21x^6+124x^5+18x^4+37x^3+21x^2+76x+147$
• $y^2=135x^6+31x^5+128x^4+34x^3+27x^2+3x+165$
• $y^2=61x^6+92x^5+50x^4+72x^3+147x^2+155x+115$
• $y^2=24x^6+67x^5+95x^4+109x^3+156x^2+13x+127$
• $y^2=147x^6+150x^5+95x^4+75x^3+105x^2+112x+96$
• $y^2=24x^6+54x^5+86x^4+118x^3+160x^2+76x+65$
• $y^2=117x^6+23x^5+147x^4+112x^3+29x^2+78x+166$
• $y^2=35x^6+43x^5+91x^4+140x^3+143x^2+113x+129$
• $y^2=28x^6+14x^5+136x^4+101x^3+86x^2+61x+141$
• $y^2=60x^6+49x^5+9x^4+95x^3+96x^2+27x+80$
• $y^2=37x^6+78x^5+21x^4+19x^3+62x^2+113x+51$
• $y^2=138x^6+53x^5+36x^4+94x^3+50x^2+111x+17$
• $y^2=53x^6+100x^5+80x^4+120x^2+58x+158$
• $y^2=82x^6+78x^5+x^4+81x^3+126x^2+23x+92$
• $y^2=146x^6+46x^5+60x^4+49x^3+55x^2+92x+45$
• $y^2=94x^6+112x^5+131x^4+39x^3+59x^2+6x+33$
• $y^2=30x^6+28x^5+10x^4+126x^3+164x^2+76x+71$
• $y^2=50x^6+127x^5+49x^4+134x^3+65x^2+122x+130$
• $y^2=24x^6+101x^5+34x^4+100x^3+163x^2+17x+107$
• $y^2=83x^6+16x^5+47x^4+63x^3+99x^2+66x+146$
• $y^2=133x^6+164x^5+39x^4+67x^3+129x^2+149x+96$
• $y^2=46x^6+59x^5+5x^4+32x^3+35x^2+52x+80$
• $y^2=79x^6+12x^5+109x^4+36x^3+34x^2+77x+45$
• $y^2=148x^6+135x^5+86x^4+142x^3+35x^2+74x+135$
• $y^2=40x^6+100x^5+154x^4+63x^3+72x^2+16x+111$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{167}$

The isogeny class factors as 1.167.ax $\times$ 1.167.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.167.ax : \(\Q(\sqrt{-139}) \).
• 1.167.av : \(\Q(\sqrt{-227}) \).

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.ac_aft	$2$	(not in LMFDB)
2.167.c_aft	$2$	(not in LMFDB)
2.167.bs_bfl	$2$	(not in LMFDB)