Abelian variety isogeny class 2.163.abs_bev over $\F_{163}$

• Label: 2.163.abs_bev
• Base field: $\F_{163}$
• 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:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 163 x^{2} )( 1 - 19 x + 163 x^{2} )$
	$1 - 44 x + 801 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0652307277549$, $\pm0.232879815243$
Angle rank:	$2$ (numerical)
Jacobians:	$40$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20155$	$697100985$	$18751177806640$	$498322461366498825$	$13239663301093020866275$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$120$	$26236$	$4329780$	$705927412$	$115063854600$	$18755369426374$	$3057125182221720$	$498311413131803428$	$81224760521510597580$	$13239635967006227806636$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 40 curves (of which all are hyperelliptic):

• $y^2=77 x^6+48 x^5+51 x^4+140 x^3+120 x^2+75 x+94$
• $y^2=72 x^6+144 x^5+124 x^4+5 x^3+141 x^2+113 x+111$
• $y^2=5 x^6+159 x^5+21 x^4+43 x^3+31 x^2+84 x+75$
• $y^2=70 x^6+125 x^5+83 x^4+78 x^3+139 x^2+35 x+84$
• $y^2=113 x^6+35 x^5+121 x^4+146 x^3+86 x^2+48 x+160$
• $y^2=72 x^6+21 x^5+19 x^4+150 x^2+8 x+105$
• $y^2=101 x^6+x^5+9 x^4+157 x^3+9 x^2+x+101$
• $y^2=12 x^6+10 x^5+154 x^4+7 x^3+89 x^2+16 x+147$
• $y^2=81 x^6+40 x^5+126 x^4+72 x^3+54 x^2+14 x+4$
• $y^2=133 x^6+20 x^5+73 x^4+136 x^3+67 x^2+107 x+120$
• $y^2=19 x^6+79 x^5+55 x^4+99 x^3+64 x^2+106 x+120$
• $y^2=29 x^6+66 x^5+46 x^4+85 x^3+41 x^2+19 x+124$
• $y^2=31 x^6+33 x^5+114 x^4+32 x^3+17 x^2+150 x+125$
• $y^2=83 x^6+10 x^5+18 x^4+124 x^3+17 x^2+40 x+78$
• $y^2=4 x^6+139 x^5+115 x^4+72 x^3+22 x^2+45 x+94$
• $y^2=46 x^6+91 x^5+55 x^4+104 x^3+115 x^2+138 x+106$
• $y^2=138 x^6+153 x^5+55 x^4+96 x^3+58 x^2+105 x+99$
• $y^2=42 x^6+50 x^5+110 x^4+126 x^3+105 x^2+64 x+148$
• $y^2=67 x^6+162 x^5+50 x^4+42 x^3+86 x^2+153 x+44$
• $y^2=130 x^6+106 x^5+5 x^4+77 x^3+108 x^2+112 x+76$
• and

• $y^2=72 x^6+30 x^5+31 x^4+93 x^3+59 x^2+66 x+55$
• $y^2=63 x^6+119 x^5+104 x^4+91 x^3+96 x^2+110 x+127$
• $y^2=103 x^6+20 x^5+156 x^4+70 x^3+14 x^2+44 x+130$
• $y^2=117 x^6+37 x^5+103 x^4+81 x^3+7 x^2+156 x+142$
• $y^2=104 x^6+102 x^5+105 x^4+21 x^3+146 x^2+84 x+107$
• $y^2=68 x^6+146 x^5+82 x^4+80 x^3+142 x^2+160 x+51$
• $y^2=45 x^6+13 x^5+148 x^4+125 x^3+63 x^2+125 x+76$
• $y^2=19 x^6+91 x^5+161 x^4+109 x^3+149 x^2+29 x+109$
• $y^2=153 x^6+72 x^5+49 x^4+109 x^3+58 x^2+155 x+67$
• $y^2=97 x^6+48 x^5+25 x^4+4 x^3+99 x^2+x+39$
• $y^2=106 x^6+35 x^5+105 x^4+22 x^3+116 x^2+8 x+159$
• $y^2=83 x^6+26 x^5+121 x^4+133 x^3+7 x^2+2 x+105$
• $y^2=27 x^6+149 x^5+15 x^4+x^3+96 x^2+59 x+138$
• $y^2=17 x^6+64 x^5+128 x^4+130 x^3+124 x^2+111 x+99$
• $y^2=2 x^6+82 x^5+94 x^4+59 x^3+149 x^2+70 x+45$
• $y^2=86 x^6+115 x^5+142 x^4+151 x^3+47 x^2+144 x+28$
• $y^2=149 x^6+150 x^5+23 x^4+96 x^3+102 x^2+58 x+120$
• $y^2=14 x^6+13 x^5+x^4+71 x^3+133 x^2+127 x+160$
• $y^2=48 x^6+62 x^5+128 x^4+60 x^3+101 x^2+74 x+13$
• $y^2=5 x^6+94 x^5+36 x^4+68 x^3+29 x^2+115 x+18$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The isogeny class factors as 1.163.az $\times$ 1.163.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.163.az : \(\Q(\sqrt{-3}) \).
• 1.163.at : \(\Q(\sqrt{-291}) \).

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
2.163.ag_aft	$2$	(not in LMFDB)
2.163.g_aft	$2$	(not in LMFDB)
2.163.bs_bev	$2$	(not in LMFDB)
2.163.al_gs	$3$	(not in LMFDB)
2.163.ac_d	$3$	(not in LMFDB)