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

• Label: 2.173.abu_bhn
• 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:	$( 1 - 25 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$
	$1 - 46 x + 871 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.100717649571$, $\pm0.205732831898$
Angle rank:	$2$ (numerical)
Jacobians:	$42$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22797$	$884637585$	$26803519496208$	$802388604578081625$	$24013930738364481950397$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$128$	$29556$	$5176706$	$895777892$	$154964685088$	$26808764337414$	$4637914433706976$	$802359179151689668$	$138808137877868610698$	$24013807852615882117236$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=166 x^6+169 x^5+148 x^4+104 x^3+85 x^2+15 x+143$
• $y^2=87 x^6+56 x^5+48 x^4+93 x^3+32 x^2+121 x+45$
• $y^2=145 x^6+154 x^5+76 x^4+28 x^3+104 x^2+101 x+104$
• $y^2=70 x^6+2 x^5+168 x^4+118 x^3+x^2+66 x+76$
• $y^2=129 x^6+25 x^5+49 x^4+95 x^3+105 x^2+141 x+34$
• $y^2=14 x^6+10 x^5+25 x^4+164 x^3+160 x^2+29 x+73$
• $y^2=95 x^6+77 x^5+61 x^4+103 x^3+97 x^2+37 x+132$
• $y^2=114 x^6+54 x^5+17 x^4+71 x^3+101 x^2+33 x+112$
• $y^2=8 x^6+63 x^5+55 x^4+87 x^3+34 x^2+2 x+5$
• $y^2=131 x^6+28 x^5+25 x^4+116 x^3+29 x^2+72 x+110$
• $y^2=15 x^6+83 x^5+121 x^4+88 x^3+16 x^2+14 x+85$
• $y^2=39 x^6+62 x^5+24 x^4+167 x^3+100 x^2+48 x+70$
• $y^2=64 x^6+158 x^5+108 x^4+51 x^3+20 x^2+60 x+132$
• $y^2=96 x^6+95 x^5+27 x^4+170 x^3+112 x^2+158 x+153$
• $y^2=172 x^6+121 x^5+37 x^4+161 x^3+119 x^2+144 x+124$
• $y^2=34 x^6+117 x^5+116 x^4+134 x^3+102 x^2+151 x+142$
• $y^2=14 x^6+102 x^5+33 x^4+80 x^3+100 x^2+119 x+2$
• $y^2=91 x^6+89 x^5+60 x^4+160 x^3+2 x^2+11 x+167$
• $y^2=171 x^6+116 x^5+169 x^4+151 x^3+140 x^2+67 x+115$
• $y^2=62 x^6+130 x^5+158 x^4+27 x^3+169 x^2+40 x+108$
• and

• $y^2=5 x^6+14 x^5+52 x^4+34 x^3+130 x^2+131 x+159$
• $y^2=87 x^6+148 x^5+133 x^4+32 x^3+119 x^2+95 x+154$
• $y^2=155 x^6+75 x^5+132 x^4+106 x^3+40 x^2+86 x+129$
• $y^2=18 x^6+124 x^5+98 x^4+144 x^3+107 x^2+119 x+94$
• $y^2=51 x^6+82 x^5+95 x^4+68 x^3+123 x^2+144 x+154$
• $y^2=48 x^6+101 x^5+32 x^4+99 x^3+65 x^2+153 x+128$
• $y^2=66 x^6+14 x^5+18 x^4+88 x^3+138 x^2+21 x+85$
• $y^2=37 x^6+171 x^5+30 x^4+148 x^3+165 x^2+26 x+36$
• $y^2=53 x^6+63 x^5+17 x^4+97 x^3+42 x^2+66 x+83$
• $y^2=124 x^6+93 x^5+161 x^4+37 x^3+33 x^2+110 x+69$
• $y^2=23 x^6+158 x^5+50 x^4+137 x^3+104 x^2+169 x+159$
• $y^2=154 x^6+27 x^5+162 x^4+32 x^3+104 x^2+101 x+8$
• $y^2=53 x^6+110 x^5+148 x^4+32 x^3+110 x^2+153 x+11$
• $y^2=34 x^6+123 x^5+134 x^4+93 x^3+42 x^2+28 x+144$
• $y^2=71 x^6+3 x^5+79 x^4+34 x^3+163 x^2+127 x+135$
• $y^2=166 x^6+35 x^5+74 x^4+84 x^3+6 x^2+100 x+101$
• $y^2=123 x^6+108 x^5+92 x^4+77 x^3+36 x^2+44 x+21$
• $y^2=102 x^6+97 x^5+133 x^4+27 x^3+3 x^2+163 x+161$
• $y^2=155 x^6+171 x^5+93 x^4+93 x^3+156 x^2+59 x+115$
• $y^2=138 x^6+20 x^5+135 x^3+146 x^2+82 x+65$
• $y^2=92 x^6+8 x^5+81 x^4+57 x^3+131 x^2+107 x+58$
• $y^2=100 x^6+143 x^5+165 x^4+143 x^3+126 x^2+65 x+12$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{173}$

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

• 1.173.az : \(\Q(\sqrt{-67}) \).
• 1.173.av : \(\Q(\sqrt{-251}) \).

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.ae_agx	$2$	(not in LMFDB)
2.173.e_agx	$2$	(not in LMFDB)
2.173.bu_bhn	$2$	(not in LMFDB)