Abelian variety isogeny class 2.173.abu_bhq over $\F_{173}$

• Label: 2.173.abu_bhq
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$
	$1 - 46 x + 874 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.134271185755$, $\pm0.184705758688$
Angle rank:	$2$ (numerical)
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22800$	$884822400$	$26805666358800$	$802401972083712000$	$24013988905912734234000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$128$	$29562$	$5177120$	$895792814$	$154965060448$	$26808771578634$	$4637914542718144$	$802359180344875486$	$138808137883549110080$	$24013807852483102291482$

Jacobians and polarizations

This isogeny class contains the Jacobians of 48 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=114x^6+84x^5+137x^4+52x^3+137x^2+84x+114$
• $y^2=113x^6+125x^5+104x^4+155x^3+104x^2+125x+113$
• $y^2=92x^6+85x^5+31x^4+133x^3+31x^2+85x+92$
• $y^2=160x^6+69x^5+101x^4+135x^3+104x^2+3x+122$
• $y^2=67x^6+32x^5+165x^4+68x^3+87x^2+65x+29$
• $y^2=85x^6+123x^5+170x^4+166x^3+170x^2+123x+85$
• $y^2=6x^6+97x^5+37x^4+5x^3+37x^2+97x+6$
• $y^2=x^6+150x^5+73x^4+2x^3+157x^2+163x+149$
• $y^2=87x^6+8x^5+72x^4+47x^3+72x^2+8x+87$
• $y^2=3x^6+58x^5+30x^4+66x^3+30x^2+58x+3$
• $y^2=106x^6+140x^5+52x^4+89x^3+121x^2+140x+67$
• $y^2=125x^6+139x^5+136x^4+112x^3+25x^2+148x+42$
• $y^2=53x^6+71x^5+90x^4+160x^3+96x^2+110x+155$
• $y^2=9x^6+43x^5+105x^4+113x^3+62x^2+164x+132$
• $y^2=71x^6+92x^5+79x^4+148x^3+79x^2+92x+71$
• $y^2=59x^6+153x^5+49x^4+49x^2+153x+59$
• $y^2=55x^6+31x^5+154x^4+162x^3+154x^2+31x+55$
• $y^2=80x^6+35x^5+57x^4+43x^3+78x^2+78x+123$
• $y^2=109x^6+79x^5+16x^4+132x^3+6x^2+3x+148$
• $y^2=154x^6+99x^5+87x^4+63x^3+154x^2+58x+70$
• and

• $y^2=78x^6+115x^5+33x^4+163x^3+33x^2+115x+78$
• $y^2=105x^6+25x^5+85x^4+130x^3+85x^2+25x+105$
• $y^2=60x^6+73x^5+92x^4+39x^3+92x^2+73x+60$
• $y^2=20x^6+164x^5+28x^4+148x^3+28x^2+164x+20$
• $y^2=92x^6+28x^5+109x^4+132x^3+109x^2+28x+92$
• $y^2=114x^6+145x^5+55x^4+140x^3+55x^2+145x+114$
• $y^2=10x^6+136x^5+39x^4+171x^3+99x^2+169x+29$
• $y^2=143x^6+x^5+21x^4+39x^3+73x^2+169x+170$
• $y^2=107x^6+63x^5+5x^4+126x^3+5x^2+63x+107$
• $y^2=115x^6+60x^5+143x^4+122x^3+68x^2+43x+65$
• $y^2=123x^6+41x^5+33x^4+43x^3+33x^2+41x+123$
• $y^2=124x^6+51x^5+143x^4+83x^3+7x^2+106x+31$
• $y^2=94x^6+154x^5+100x^4+34x^3+100x^2+154x+94$
• $y^2=58x^6+155x^5+140x^4+12x^3+9x^2+63x+134$
• $y^2=98x^6+156x^5+23x^4+158x^3+4x^2+42x+107$
• $y^2=138x^6+10x^5+15x^4+33x^3+77x^2+29x+96$
• $y^2=89x^6+87x^5+65x^4+5x^3+65x^2+87x+89$
• $y^2=88x^6+119x^5+56x^4+26x^3+159x^2+148x+150$
• $y^2=112x^6+74x^5+138x^4+150x^3+40x^2+79x+27$
• $y^2=63x^6+164x^5+113x^4+100x^3+113x^2+164x+63$
• $y^2=50x^6+110x^5+54x^4+13x^3+133x^2+53x+147$
• $y^2=83x^6+140x^5+67x^4+134x^3+67x^2+140x+83$
• $y^2=61x^6+73x^5+153x^4+22x^3+153x^2+73x+61$
• $y^2=161x^6+72x^5+147x^4+24x^3+63x^2+45x+108$
• $y^2=75x^6+136x^5+51x^4+131x^3+10x^2+133x+28$
• $y^2=76x^6+135x^5+22x^4+140x^3+22x^2+135x+76$
• $y^2=37x^6+98x^5+17x^4+165x^3+143x^2+128x+144$
• $y^2=141x^6+58x^5+57x^4+3x^3+57x^2+58x+141$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The isogeny class factors as 1.173.ay $\times$ 1.173.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.173.ay : \(\Q(\sqrt{-29}) \).
• 1.173.aw : \(\Q(\sqrt{-13}) \).

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
2.173.ac_aha	$2$	(not in LMFDB)
2.173.c_aha	$2$	(not in LMFDB)
2.173.bu_bhq	$2$	(not in LMFDB)