Abelian variety isogeny class 2.167.abu_bhe over $\F_{167}$

• Label: 2.167.abu_bhe
• Base field: $\F_{167}$
• 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:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 167 x^{2} )( 1 - 22 x + 167 x^{2} )$
	$1 - 46 x + 862 x^{2} - 7682 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.121023609245$, $\pm0.175872025744$
Angle rank:	$2$ (numerical)
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21024$	$766955520$	$21685328694432$	$604990834989465600$	$16872045268985848665504$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$122$	$27498$	$4656038$	$777826814$	$129892889002$	$21691976846346$	$3622557783376150$	$604967118957133246$	$101029508546654492186$	$16871927924945588746218$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):

• $y^2=91 x^6+157 x^5+46 x^4+107 x^3+46 x^2+157 x+91$
• $y^2=16 x^6+94 x^5+77 x^4+164 x^3+77 x^2+94 x+16$
• $y^2=77 x^6+98 x^5+18 x^4+67 x^3+18 x^2+98 x+77$
• $y^2=152 x^6+56 x^5+140 x^4+136 x^3+43 x^2+126 x+12$
• $y^2=158 x^6+55 x^5+128 x^4+35 x^3+126 x^2+80 x+82$
• $y^2=29 x^6+73 x^5+29 x^4+127 x^3+147 x^2+135 x+114$
• $y^2=106 x^6+85 x^5+136 x^4+79 x^3+151 x^2+11 x+69$
• $y^2=43 x^6+65 x^5+87 x^4+32 x^3+7 x^2+93 x+10$
• $y^2=66 x^6+150 x^5+74 x^4+149 x^3+74 x^2+150 x+66$
• $y^2=101 x^6+78 x^5+15 x^4+116 x^3+83 x^2+68 x+73$
• $y^2=35 x^6+141 x^5+23 x^4+18 x^3+35 x^2+115 x+92$
• $y^2=107 x^6+119 x^5+20 x^4+124 x^3+20 x^2+119 x+107$
• $y^2=41 x^6+39 x^5+42 x^4+97 x^3+3 x^2+105 x+40$
• $y^2=150 x^6+131 x^5+136 x^4+11 x^3+83 x^2+155 x+87$
• $y^2=143 x^6+86 x^5+120 x^4+3 x^3+120 x^2+86 x+143$
• $y^2=30 x^6+98 x^5+128 x^4+74 x^3+128 x^2+98 x+30$
• $y^2=129 x^6+8 x^5+62 x^4+104 x^3+62 x^2+8 x+129$
• $y^2=125 x^6+72 x^5+97 x^4+50 x^3+62 x^2+162 x+67$
• $y^2=129 x^6+44 x^5+108 x^4+108 x^3+108 x^2+44 x+129$
• $y^2=85 x^6+143 x^5+100 x^4+14 x^3+100 x^2+143 x+85$
• $y^2=143 x^6+106 x^5+132 x^4+28 x^3+121 x^2+45 x+123$
• $y^2=74 x^6+30 x^5+10 x^4+26 x^3+10 x^2+30 x+74$
• $y^2=55 x^6+119 x^5+110 x^4+59 x^3+45 x^2+101 x+104$
• $y^2=62 x^6+57 x^5+26 x^4+39 x^3+26 x^2+57 x+62$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$

The isogeny class factors as 1.167.ay $\times$ 1.167.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.167.ay : \(\Q(\sqrt{-23}) \).
• 1.167.aw : \(\Q(\sqrt{-46}) \).

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
2.167.ac_ahm	$2$	(not in LMFDB)
2.167.c_ahm	$2$	(not in LMFDB)
2.167.bu_bhe	$2$	(not in LMFDB)