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 is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

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

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)