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 contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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)