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

• Label: 2.173.abu_bhi
• 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:	$( 1 - 26 x + 173 x^{2} )( 1 - 20 x + 173 x^{2} )$
	$1 - 46 x + 866 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0485897903475$, $\pm0.225058830207$
Angle rank:	$2$ (numerical)
Jacobians:	$36$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22792$	$884329600$	$26799941496328$	$802366253860864000$	$24013832366865170070472$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$128$	$29546$	$5176016$	$895752942$	$154964050288$	$26808751715834$	$4637914228914976$	$802359176411562718$	$138808137848265316448$	$24013807852378475042186$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=168 x^6+54 x^5+120 x^4+108 x^3+25 x^2+19 x+166$
• $y^2=97 x^6+60 x^5+69 x^4+107 x^3+38 x^2+61 x+76$
• $y^2=131 x^6+15 x^5+68 x^4+46 x^3+68 x^2+15 x+131$
• $y^2=99 x^6+153 x^5+139 x^4+15 x^3+118 x^2+56 x+41$
• $y^2=102 x^6+22 x^5+70 x^4+7 x^3+70 x^2+22 x+102$
• $y^2=6 x^6+136 x^5+134 x^4+69 x^3+110 x^2+163 x+169$
• $y^2=82 x^6+99 x^5+120 x^4+58 x^3+14 x^2+68 x+108$
• $y^2=116 x^6+103 x^5+90 x^4+58 x^3+135 x^2+40 x+80$
• $y^2=x^6+78 x^5+124 x^4+48 x^3+47 x^2+148 x+16$
• $y^2=127 x^6+31 x^5+118 x^4+126 x^3+80 x^2+29 x+98$
• $y^2=131 x^6+9 x^5+14 x^4+61 x^3+121 x^2+124 x+142$
• $y^2=6 x^6+22 x^5+106 x^4+83 x^3+107 x^2+102 x+93$
• $y^2=42 x^6+82 x^5+120 x^4+63 x^3+70 x^2+32 x+128$
• $y^2=66 x^6+15 x^5+68 x^4+88 x^2+59 x+152$
• $y^2=99 x^6+142 x^5+94 x^4+69 x^3+25 x^2+81 x+77$
• $y^2=110 x^6+66 x^5+116 x^4+9 x^3+55 x^2+78 x+19$
• $y^2=44 x^6+122 x^5+165 x^4+97 x^3+114 x^2+31 x+113$
• $y^2=124 x^6+153 x^5+111 x^4+49 x^3+51 x^2+83 x+142$
• $y^2=29 x^6+157 x^5+24 x^4+74 x^3+49 x^2+55 x+142$
• $y^2=104 x^6+126 x^5+171 x^4+76 x^3+118 x^2+34 x+96$
• and

• $y^2=92 x^6+14 x^5+152 x^4+24 x^3+8 x^2+161 x+170$
• $y^2=71 x^6+61 x^5+133 x^4+115 x^3+133 x^2+61 x+71$
• $y^2=36 x^6+149 x^5+9 x^4+53 x^3+168 x^2+143 x+2$
• $y^2=95 x^6+101 x^5+83 x^4+4 x^3+131 x^2+124 x+50$
• $y^2=145 x^6+31 x^5+55 x^4+105 x^3+24 x^2+89 x+171$
• $y^2=77 x^6+100 x^5+104 x^4+88 x^3+51 x^2+141 x+105$
• $y^2=92 x^6+59 x^5+56 x^4+60 x^3+157 x^2+74 x+97$
• $y^2=66 x^6+29 x^5+155 x^4+31 x^3+152 x^2+85 x+146$
• $y^2=132 x^6+103 x^5+21 x^4+169 x^3+83 x^2+123 x+9$
• $y^2=12 x^6+111 x^5+47 x^4+36 x^3+17 x^2+25 x+26$
• $y^2=105 x^6+115 x^5+29 x^4+5 x^3+153 x^2+172 x+156$
• $y^2=88 x^6+45 x^5+132 x^4+22 x^3+43 x^2+164 x+101$
• $y^2=135 x^6+88 x^5+90 x^4+73 x^3+160 x^2+56 x+137$
• $y^2=78 x^6+59 x^5+63 x^4+26 x^3+114 x^2+118 x+30$
• $y^2=143 x^6+54 x^5+146 x^4+45 x^3+74 x^2+34 x+155$
• $y^2=77 x^6+11 x^5+52 x^4+73 x^3+52 x^2+11 x+77$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{173}$

The isogeny class factors as 1.173.aba $\times$ 1.173.au 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.aba : \(\Q(\sqrt{-1}) \).
• 1.173.au : \(\Q(\sqrt{-73}) \).

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.ag_ags	$2$	(not in LMFDB)
2.173.g_ags	$2$	(not in LMFDB)
2.173.bu_bhi	$2$	(not in LMFDB)