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 contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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)