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

• Label: 2.173.abw_bjm
• 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:	$( 1 - 24 x + 173 x^{2} )^{2}$
	$1 - 48 x + 922 x^{2} - 8304 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.134271185755$, $\pm0.134271185755$
Angle rank:	$1$ (numerical)
Jacobians:	$39$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22500$	$882090000$	$26794599322500$	$802371645504000000$	$24013932957293468062500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$126$	$29470$	$5174982$	$895758958$	$154964699406$	$26808770300110$	$4637914594018902$	$802359181962244318$	$138808137913742345886$	$24013807852904927156350$

Jacobians and polarizations

This isogeny class contains the Jacobians of 39 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=165x^6+139x^5+136x^4+151x^3+14x^2+6x+63$
• $y^2=71x^6+76x^5+78x^4+27x^3+78x^2+76x+71$
• $y^2=129x^6+103x^5+59x^4+142x^3+2x^2+146x+42$
• $y^2=8x^6+145x^5+29x^4+63x^3+119x^2+115x+68$
• $y^2=150x^6+100x^5+62x^4+95x^3+153x^2+133x+64$
• $y^2=98x^6+149x^5+134x^4+99x^3+2x^2+118x+143$
• $y^2=59x^6+86x^5+160x^4+121x^3+100x^2+39x+108$
• $y^2=33x^6+170x^5+26x^4+49x^3+21x^2+152x+137$
• $y^2=92x^6+14x^5+120x^4+8x^3+161x^2+142x+139$
• $y^2=38x^6+x^5+43x^4+120x^3+43x^2+x+38$
• $y^2=44x^6+122x^5+50x^4+46x^3+93x^2+167x+8$
• $y^2=65x^6+93x^5+94x^4+10x^3+32x^2+166x+105$
• $y^2=170x^6+31x^4+31x^2+170$
• $y^2=96x^6+132x^5+12x^4+60x^3+12x^2+132x+96$
• $y^2=170x^6+18x^5+120x^4+86x^3+125x^2+79x+86$
• $y^2=103x^6+4x^5+47x^4+111x^3+47x^2+4x+103$
• $y^2=167x^6+56x^5+39x^4+64x^3+79x^2+172x+14$
• $y^2=84x^6+90x^5+87x^4+67x^3+26x^2+122x+16$
• $y^2=92x^6+158x^5+3x^4+49x^3+3x^2+158x+92$
• $y^2=101x^6+94x^5+66x^4+35x^3+26x^2+91x+5$
• and

• $y^2=96x^6+33x^5+159x^4+35x^3+164x^2+41x+25$
• $y^2=60x^6+91x^5+134x^4+131x^3+134x^2+91x+60$
• $y^2=27x^6+40x^5+110x^4+121x^3+132x^2+18x+66$
• $y^2=127x^6+170x^5+108x^4+94x^3+161x^2+32x+48$
• $y^2=160x^6+46x^5+86x^4+17x^3+27x^2+61x+96$
• $y^2=58x^6+110x^5+76x^4+38x^3+76x^2+110x+58$
• $y^2=62x^6+61x^5+42x^4+137x^3+45x^2+168x+61$
• $y^2=19x^6+90x^5+125x^4+4x^3+125x^2+90x+19$
• $y^2=156x^6+93x^4+93x^2+156$
• $y^2=114x^6+150x^5+73x^4+67x^3+73x^2+150x+114$
• $y^2=165x^6+151x^5+84x^4+69x^3+84x^2+151x+165$
• $y^2=108x^6+72x^5+107x^4+132x^3+60x^2+7x+21$
• $y^2=30x^6+39x^4+39x^2+30$
• $y^2=33x^6+8x^5+44x^4+155x^3+73x^2+5x+89$
• $y^2=63x^6+68x^5+65x^4+132x^3+74x^2+72x+89$
• $y^2=65x^6+101x^5+122x^4+69x^3+122x^2+101x+65$
• $y^2=3x^6+120x^5+129x^4+49x^3+94x^2+63x+114$
• $y^2=68x^6+105x^5+123x^4+140x^3+63x^2+93x+3$
• $y^2=12x^6+5x^5+162x^4+98x^3+162x^2+5x+12$

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^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-29}) \)$)$

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
2.173.a_aiw	$2$	(not in LMFDB)
2.173.bw_bjm	$2$	(not in LMFDB)
2.173.y_pn	$3$	(not in LMFDB)