Abelian variety isogeny class 2.179.abu_bht over $\F_{179}$

• Label: 2.179.abu_bht
• Base field: $\F_{179}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{179}$
Dimension:	$2$
L-polynomial:	$1 - 46 x + 877 x^{2} - 8234 x^{3} + 32041 x^{4}$
Frobenius angles:	$\pm0.0673026795343$, $\pm0.234176157399$
Angle rank:	$2$ (numerical)
Number field:	4.0.16270400.1
Galois group:	$D_{4}$
Jacobians:	$18$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24639$	$1015102161$	$32888309771556$	$1053981151359429609$	$33769999597085204997399$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$31680$	$5734328$	$1026646004$	$183766312414$	$32894113402206$	$5888046227726986$	$1053960287242942564$	$188658891694120647992$	$33769941616298091481200$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

• $y^2=33 x^6+72 x^5+61 x^4+103 x^3+20 x^2+152 x+25$
• $y^2=55 x^6+133 x^5+54 x^4+127 x^3+48 x^2+63 x+59$
• $y^2=128 x^6+81 x^5+44 x^4+20 x^3+51 x^2+31 x+140$
• $y^2=104 x^6+23 x^5+19 x^4+67 x^3+51 x^2+80 x+20$
• $y^2=103 x^6+94 x^5+86 x^4+131 x^3+109 x^2+94 x+97$
• $y^2=4 x^6+177 x^5+73 x^4+161 x^3+9 x^2+57 x+178$
• $y^2=176 x^6+141 x^5+171 x^4+96 x^3+175 x^2+17 x+134$
• $y^2=80 x^6+41 x^5+139 x^4+62 x^3+16 x^2+85 x+58$
• $y^2=147 x^6+17 x^5+32 x^4+145 x^3+177 x^2+40 x+129$
• $y^2=46 x^6+66 x^5+109 x^4+127 x^3+15 x^2+103 x+133$
• $y^2=115 x^6+160 x^5+x^4+25 x^3+139 x^2+52 x+97$
• $y^2=94 x^6+12 x^5+125 x^4+118 x^3+86 x^2+132 x+30$
• $y^2=36 x^6+120 x^5+100 x^4+58 x^3+8 x^2+14 x+26$
• $y^2=84 x^6+159 x^5+2 x^4+56 x^3+151 x^2+123 x+40$
• $y^2=6 x^6+40 x^5+66 x^4+26 x^3+131 x^2+175 x+154$
• $y^2=63 x^6+138 x^5+165 x^4+120 x^3+74 x^2+18 x+63$
• $y^2=63 x^6+46 x^5+162 x^4+50 x^3+76 x^2+92 x+53$
• $y^2=164 x^6+39 x^5+168 x^4+95 x^3+160 x^2+147 x+91$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{179}$.

Endomorphism algebra over $\F_{179}$

The endomorphism algebra of this simple isogeny class is 4.0.16270400.1.

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
2.179.bu_bht	$2$	(not in LMFDB)