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

• Label: 2.191.aby_bmp
• 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:	$( 1 - 27 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$
	$1 - 50 x + 1003 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0686610702072$, $\pm0.187132320568$
Angle rank:	$2$ (numerical)
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27885$	$1312965225$	$48528938755440$	$1771202484229689225$	$64615178135059740742125$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$142$	$35988$	$6964672$	$1330867268$	$254195413202$	$48551235379038$	$9273284314651982$	$1771197286087321348$	$338298681552776456512$	$64615048177692355395348$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=183x^6+157x^5+48x^4+111x^3+38x^2+157x+145$
• $y^2=188x^6+144x^5+161x^4+133x^3+35x^2+23x+4$
• $y^2=44x^6+82x^5+162x^4+68x^3+162x^2+82x+44$
• $y^2=172x^6+160x^5+83x^4+52x^3+158x^2+94x+103$
• $y^2=139x^6+62x^5+110x^4+171x^3+110x^2+62x+139$
• $y^2=107x^6+111x^5+186x^4+114x^3+73x^2+32x+148$
• $y^2=132x^6+64x^5+86x^4+143x^3+107x^2+37x+98$
• $y^2=105x^6+117x^5+161x^4+137x^3+51x^2+54x+19$
• $y^2=22x^6+25x^5+66x^4+170x^3+66x^2+25x+22$
• $y^2=42x^6+32x^5+112x^4+141x^3+112x^2+32x+42$
• $y^2=65x^6+23x^5+39x^4+83x^3+173x^2+136x+4$
• $y^2=28x^6+23x^5+66x^4+187x^3+66x^2+23x+28$
• $y^2=148x^6+101x^5+56x^4+141x^3+56x^2+101x+148$
• $y^2=178x^6+103x^5+143x^4+75x^3+143x^2+103x+178$
• $y^2=188x^6+163x^5+20x^4+179x^3+115x^2+26x+186$
• $y^2=160x^6+167x^5+141x^4+145x^3+149x^2+99x+160$
• $y^2=121x^6+25x^5+30x^4+27x^3+30x^2+25x+121$
• $y^2=136x^6+184x^5+95x^4+85x^3+95x^2+184x+136$
• $y^2=60x^6+188x^5+6x^4+150x^3+51x^2+130x+73$
• $y^2=111x^6+112x^5+13x^4+56x^3+36x^2+139x+184$
• $y^2=144x^6+89x^5+128x^4+119x^3+128x^2+89x+144$
• $y^2=163x^6+92x^5+138x^4+135x^3+138x^2+92x+163$
• $y^2=11x^6+110x^5+182x^4+10x^3+3x^2+180x+74$
• $y^2=62x^6+180x^5+43x^4+49x^3+43x^2+180x+62$

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.ax 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.ax : \(\Q(\sqrt{-235}) \).

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_ajf	$2$	(not in LMFDB)
2.191.e_ajf	$2$	(not in LMFDB)
2.191.by_bmp	$2$	(not in LMFDB)