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

• Label: 2.191.abx_blp
• Base field: $\F_{191}$
• 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:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$1 - 49 x + 977 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0791099210161$, $\pm0.202977754945$
Angle rank:	$2$ (numerical)
Number field:	4.0.5519997.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28051$	$1314666217$	$48536552030425$	$1771224979839254125$	$64615221609140484836656$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$143$	$36035$	$6965765$	$1330884171$	$254195584228$	$48551235961367$	$9273284297855203$	$1771197285721877731$	$338298681550827579605$	$64615048177775117121230$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which all are hyperelliptic):

• $y^2=154 x^6+122 x^5+170 x^4+123 x^3+24 x^2+40 x+144$
• $y^2=123 x^6+57 x^5+176 x^4+125 x^3+69 x^2+102 x+183$
• $y^2=141 x^6+65 x^5+23 x^4+17 x^3+139 x^2+53 x+188$
• $y^2=187 x^6+127 x^5+100 x^4+150 x^3+27 x^2+73 x+31$
• $y^2=79 x^6+58 x^5+148 x^4+10 x^3+163 x^2+57 x+118$
• $y^2=45 x^6+3 x^5+171 x^4+115 x^3+75 x^2+3 x+46$
• $y^2=148 x^6+184 x^5+128 x^4+3 x^3+144 x^2+130 x+44$
• $y^2=74 x^6+82 x^5+27 x^4+38 x^3+92 x^2+95 x+55$
• $y^2=134 x^6+9 x^5+32 x^4+84 x^3+136 x^2+41 x+135$
• $y^2=168 x^6+141 x^5+71 x^4+171 x^3+59 x^2+14 x+111$
• $y^2=23 x^6+84 x^5+4 x^4+50 x^3+154 x^2+23 x+152$
• $y^2=33 x^6+23 x^5+153 x^4+181 x^3+187 x^2+152 x+98$
• $y^2=2 x^6+57 x^5+13 x^4+171 x^3+122 x^2+56 x+75$
• $y^2=44 x^6+138 x^5+182 x^4+59 x^3+44 x^2+187 x+143$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{191}$

The endomorphism algebra of this simple isogeny class is 4.0.5519997.1.

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
2.191.bx_blp	$2$	(not in LMFDB)