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

• Label: 2.173.abt_bgh
• Base field: $\F_{173}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 839 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0357609426795$, $\pm0.245538694866$
Angle rank:	$2$ (numerical)
Number field:	4.0.8216325.2
Galois group:	$D_{4}$
Jacobians:	$16$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22939$	$885422461$	$26802459532471$	$802364416258161141$	$24013796695124629472464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$129$	$29583$	$5176503$	$895750891$	$154963820094$	$26808746111367$	$4637914143825063$	$802359175580518483$	$138808137845228121369$	$24013807852433588560278$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=56x^6+128x^5+82x^4+129x^3+6x^2+8x+90$
• $y^2=53x^6+100x^5+120x^4+79x^3+97x^2+130x+140$
• $y^2=114x^6+99x^5+46x^4+106x^3+59x^2+50x+80$
• $y^2=145x^6+73x^5+23x^4+101x^3+131x^2+160x+129$
• $y^2=93x^6+57x^5+121x^4+58x^3+87x^2+69x+82$
• $y^2=145x^6+22x^5+35x^4+34x^3+13x^2+155x+77$
• $y^2=63x^6+46x^5+101x^4+61x^3+129x^2+31x+163$
• $y^2=40x^6+93x^5+10x^4+43x^3+102x^2+21x+73$
• $y^2=125x^6+166x^5+6x^4+38x^3+56x^2+98x+166$
• $y^2=61x^6+8x^5+130x^4+30x^3+147x^2+2x+139$
• $y^2=166x^6+88x^5+107x^4+35x^3+168x^2+153x+54$
• $y^2=3x^6+51x^5+16x^4+23x^3+2x^2+92x+59$
• $y^2=57x^6+161x^5+4x^4+53x^3+6x^2+146x+79$
• $y^2=104x^6+108x^5+42x^4+111x^3+136x^2+171x$
• $y^2=134x^6+136x^5+55x^4+109x^3+128x^2+166x+42$
• $y^2=20x^6+62x^5+24x^4+26x^3+88x^2+39x+107$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is 4.0.8216325.2.

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
2.173.bt_bgh	$2$	(not in LMFDB)