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

• Label: 2.191.abv_bjm
• 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:	$( 1 - 27 x + 191 x^{2} )( 1 - 20 x + 191 x^{2} )$
	$1 - 47 x + 922 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0686610702072$, $\pm0.242497774430$
Angle rank:	$2$ (numerical)
Jacobians:	$56$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28380$	$1317626640$	$48545985795120$	$1771230810646440000$	$64615128331508560294500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36117$	$6967120$	$1330888553$	$254195217275$	$48551224431582$	$9273284094390125$	$1771197283448172913$	$338298681541989714160$	$64615048178041051967277$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=82 x^6+163 x^5+13 x^4+68 x^3+171 x^2+160 x+186$
• $y^2=158 x^6+65 x^5+93 x^4+106 x^3+97 x^2+84 x+51$
• $y^2=4 x^6+160 x^5+126 x^4+49 x^3+36 x^2+138 x+22$
• $y^2=164 x^6+13 x^5+11 x^4+126 x^3+29 x^2+103 x+134$
• $y^2=140 x^6+115 x^5+12 x^4+67 x^3+133 x^2+124 x+153$
• $y^2=6 x^6+189 x^5+135 x^4+130 x^3+65 x^2+125 x+23$
• $y^2=169 x^6+53 x^5+60 x^4+124 x^3+59 x^2+97 x+26$
• $y^2=121 x^6+62 x^5+31 x^4+68 x^3+111 x^2+147 x+141$
• $y^2=158 x^6+62 x^5+177 x^4+42 x^3+108 x^2+68 x+145$
• $y^2=43 x^6+116 x^5+29 x^4+117 x^3+15 x^2+112 x+6$
• $y^2=55 x^6+13 x^5+83 x^4+70 x^3+130 x^2+40 x+114$
• $y^2=122 x^6+143 x^5+35 x^4+109 x^3+150 x^2+181 x+21$
• $y^2=91 x^6+39 x^5+21 x^4+16 x^3+105 x^2+140 x+121$
• $y^2=57 x^6+117 x^5+10 x^4+61 x^3+24 x^2+65 x+29$
• $y^2=175 x^6+155 x^5+79 x^4+62 x^3+65 x^2+46 x+6$
• $y^2=60 x^6+63 x^5+20 x^4+110 x^3+89 x^2+65 x+189$
• $y^2=x^6+174 x^5+6 x^4+63 x^3+183 x^2+10 x+158$
• $y^2=61 x^6+55 x^5+2 x^4+17 x^3+36 x^2+58 x+157$
• $y^2=152 x^6+10 x^5+124 x^4+51 x^3+23 x^2+107 x+147$
• $y^2=110 x^6+10 x^5+82 x^4+95 x^3+151 x^2+11 x+36$
• and

• $y^2=180 x^6+129 x^5+111 x^4+66 x^3+17 x^2+108 x+35$
• $y^2=29 x^6+156 x^5+104 x^4+102 x^3+13 x^2+155 x+153$
• $y^2=42 x^6+177 x^5+176 x^4+164 x^3+148 x^2+187 x+178$
• $y^2=142 x^6+103 x^5+90 x^4+126 x^3+105 x^2+53 x+127$
• $y^2=154 x^6+76 x^5+185 x^4+18 x^3+57 x^2+136 x+129$
• $y^2=x^6+2 x^5+127 x^4+58 x^3+176 x^2+89 x+165$
• $y^2=137 x^6+39 x^5+163 x^4+146 x^3+26 x^2+119 x+84$
• $y^2=149 x^6+42 x^5+24 x^4+15 x^3+42 x^2+94 x+80$
• $y^2=171 x^6+167 x^5+159 x^4+61 x^3+108 x^2+159 x+173$
• $y^2=19 x^6+127 x^5+88 x^4+156 x^3+12 x^2+137 x+119$
• $y^2=141 x^6+24 x^5+75 x^4+40 x^3+146 x^2+89 x+187$
• $y^2=96 x^6+100 x^5+30 x^4+127 x^3+7 x^2+82 x+57$
• $y^2=70 x^6+81 x^5+63 x^4+47 x^3+28 x^2+90 x+76$
• $y^2=5 x^6+164 x^5+86 x^4+172 x^3+182 x^2+179 x+155$
• $y^2=77 x^6+95 x^5+75 x^4+19 x^3+146 x^2+96 x+17$
• $y^2=43 x^6+54 x^5+57 x^4+152 x^3+21 x^2+125 x+143$
• $y^2=169 x^6+33 x^5+182 x^4+179 x^3+160 x^2+159 x+144$
• $y^2=189 x^6+173 x^5+63 x^4+24 x^3+155 x^2+145 x+89$
• $y^2=93 x^6+87 x^5+57 x^4+18 x^3+155 x^2+24 x+132$
• $y^2=62 x^6+74 x^5+159 x^4+160 x^3+83 x^2+27 x+188$
• $y^2=167 x^6+132 x^5+76 x^4+182 x^3+163 x^2+82 x+117$
• $y^2=129 x^6+70 x^5+93 x^4+91 x^3+45 x^2+49 x+81$
• $y^2=85 x^6+82 x^5+43 x^4+88 x^3+105 x^2+86 x+7$
• $y^2=104 x^6+29 x^5+130 x^4+80 x^3+14 x^2+145 x+142$
• $y^2=107 x^6+64 x^5+152 x^4+12 x^3+138 x^2+85 x+181$
• $y^2=18 x^6+143 x^5+92 x^4+x^3+60 x^2+172 x+83$
• $y^2=121 x^6+130 x^5+126 x^4+167 x^3+67 x^2+108 x+61$
• $y^2=15 x^6+152 x^5+26 x^4+151 x^3+130 x^2+114 x+150$
• $y^2=155 x^6+29 x^5+151 x^4+5 x^3+66 x^2+161 x+28$
• $y^2=157 x^6+18 x^5+9 x^4+111 x^3+57 x^2+162 x+147$
• $y^2=109 x^6+169 x^5+90 x^4+107 x^3+81 x^2+100 x+6$
• $y^2=133 x^6+76 x^5+57 x^4+10 x^3+150 x^2+138 x+55$
• $y^2=56 x^6+146 x^5+149 x^4+29 x^3+66 x^2+74 x+126$
• $y^2=159 x^6+36 x^5+15 x^4+51 x^3+20 x^2+52 x+184$
• $y^2=188 x^6+104 x^5+33 x^4+110 x^3+106 x^2+20 x+5$
• $y^2=152 x^6+171 x^5+133 x^4+16 x^3+145 x^2+135 x+92$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.abb $\times$ 1.191.au 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.abb : \(\Q(\sqrt{-35}) \).
• 1.191.au : \(\Q(\sqrt{-91}) \).

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.ah_agc	$2$	(not in LMFDB)
2.191.h_agc	$2$	(not in LMFDB)
2.191.bv_bjm	$2$	(not in LMFDB)