Abelian variety isogeny class 2.191.abw_bks over $\F_{191}$

• Label: 2.191.abw_bks
• Base field: $\F_{191}$
• 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:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$
	$1 - 48 x + 954 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.110219473395$, $\pm0.206981219725$
Angle rank:	$2$ (numerical)
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28220$	$1316519440$	$48546218097020$	$1771262611568296960$	$64615343927199401685500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36086$	$6967152$	$1330912446$	$254196065424$	$48551243138678$	$9273284393960304$	$1771197286880617726$	$338298681562924658832$	$64615048177864704875126$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which all are hyperelliptic):

• $y^2=131 x^6+86 x^5+87 x^4+92 x^3+187 x^2+177 x+176$
• $y^2=38 x^6+27 x^5+189 x^4+55 x^3+165 x^2+135 x+85$
• $y^2=190 x^6+41 x^5+7 x^4+81 x^3+113 x^2+36 x+92$
• $y^2=93 x^6+101 x^5+36 x^4+122 x^3+60 x^2+157 x+140$
• $y^2=35 x^6+127 x^5+78 x^4+113 x^3+15 x^2+105 x+91$
• $y^2=92 x^6+66 x^5+106 x^4+154 x^3+106 x^2+66 x+92$
• $y^2=24 x^6+112 x^5+187 x^4+167 x^3+21 x^2+6 x+170$
• $y^2=176 x^6+151 x^5+164 x^4+79 x^3+164 x^2+151 x+176$
• $y^2=124 x^6+45 x^5+48 x^4+57 x^3+104 x^2+48 x+50$
• $y^2=116 x^6+171 x^5+39 x^4+40 x^3+172 x^2+131 x+139$
• $y^2=155 x^6+124 x^5+77 x^4+150 x^3+136 x^2+188 x+105$
• $y^2=188 x^6+181 x^5+178 x^4+86 x^3+x^2+179 x+50$
• $y^2=149 x^6+112 x^5+190 x^4+27 x^3+190 x^2+112 x+149$
• $y^2=4 x^6+172 x^5+98 x^4+83 x^3+136 x^2+163 x+1$
• $y^2=49 x^6+132 x^5+11 x^4+149 x^3+14 x^2+64 x+117$
• $y^2=93 x^6+102 x^5+59 x^4+58 x^3+163 x^2+185 x+36$
• $y^2=162 x^6+51 x^5+155 x^4+17 x^3+45 x^2+164 x+145$
• $y^2=7 x^6+116 x^5+58 x^4+155 x^3+142 x^2+33 x+124$
• $y^2=171 x^6+168 x^5+86 x^4+69 x^3+86 x^2+168 x+171$
• $y^2=45 x^6+6 x^5+169 x^4+54 x^3+126 x^2+132 x+142$
• and

• $y^2=167 x^6+70 x^5+182 x^4+78 x^3+128 x^2+73 x+174$
• $y^2=186 x^6+107 x^5+137 x^4+180 x^3+137 x^2+107 x+186$
• $y^2=189 x^6+144 x^5+136 x^4+132 x^3+92 x^2+54 x+161$
• $y^2=136 x^6+24 x^5+179 x^4+131 x^3+57 x^2+64 x+60$
• $y^2=126 x^6+117 x^5+43 x^4+23 x^3+101 x^2+75 x+42$
• $y^2=179 x^6+15 x^5+122 x^4+136 x^3+176 x^2+100 x+157$
• $y^2=7 x^6+30 x^5+19 x^4+137 x^3+19 x^2+30 x+7$
• $y^2=189 x^6+157 x^5+29 x^4+14 x^3+173 x^2+61 x+160$
• $y^2=119 x^6+171 x^5+93 x^4+8 x^3+93 x^2+171 x+119$
• $y^2=94 x^6+66 x^5+8 x^4+181 x^3+138 x^2+17 x+148$
• $y^2=174 x^6+84 x^5+55 x^3+83 x^2+24 x+150$
• $y^2=181 x^6+57 x^5+50 x^4+17 x^3+50 x^2+57 x+181$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{191}$.

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.aba $\times$ 1.191.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.191.aba : \(\Q(\sqrt{-22}) \).
• 1.191.aw : \(\Q(\sqrt{-70}) \).

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
2.191.ae_ahi	$2$	(not in LMFDB)
2.191.e_ahi	$2$	(not in LMFDB)
2.191.bw_bks	$2$	(not in LMFDB)