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

• Label: 2.191.abv_bjn
• 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:	$1 - 47 x + 923 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0761135416416$, $\pm0.240053756085$
Angle rank:	$2$ (numerical)
Number field:	4.0.383725.4
Galois group:	$D_{4}$
Jacobians:	$27$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28381$	$1317701449$	$48546969442891$	$1771237659671215069$	$64615161484954782005776$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36119$	$6967261$	$1330893699$	$254195347700$	$48551226979403$	$9273284134491935$	$1771197283966254259$	$338298681547563005791$	$64615048178094058525454$

Jacobians and polarizations

This isogeny class contains the Jacobians of 27 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=42x^6+120x^5+19x^4+156x^2+50x+181$
• $y^2=151x^6+154x^5+188x^4+2x^3+92x^2+179x+63$
• $y^2=152x^6+34x^5+168x^4+152x^3+108x^2+87x+84$
• $y^2=123x^6+36x^5+188x^4+70x^3+58x^2+118x+157$
• $y^2=156x^6+179x^5+11x^4+118x^3+21x^2+78x+72$
• $y^2=167x^6+180x^5+113x^4+43x^3+95x^2+179x+7$
• $y^2=56x^6+85x^5+140x^4+140x^3+176x^2+76x+74$
• $y^2=184x^6+120x^5+67x^4+170x^3+124x^2+77x+28$
• $y^2=23x^6+66x^5+109x^4+9x^3+22x^2+109x+8$
• $y^2=21x^6+112x^5+156x^4+101x^3+167x^2+126x+2$
• $y^2=105x^6+44x^5+3x^4+97x^3+134x^2+98x+168$
• $y^2=179x^6+135x^4+150x^3+49x^2+19x+159$
• $y^2=22x^6+152x^5+19x^4+62x^3+36x^2+93x+179$
• $y^2=11x^6+34x^5+119x^4+181x^3+47x^2+135x+42$
• $y^2=147x^6+99x^5+130x^4+174x^3+140x^2+66x+167$
• $y^2=64x^6+31x^5+103x^4+68x^3+66x^2+126x+111$
• $y^2=7x^6+114x^5+130x^4+135x^3+128x^2+86x+163$
• $y^2=165x^6+67x^5+28x^4+120x^3+111x^2+50x+12$
• $y^2=122x^6+104x^5+24x^4+103x^3+39x^2+189x+122$
• $y^2=162x^6+131x^5+23x^4+48x^3+188x^2+176x+92$
• $y^2=19x^6+41x^5+154x^4+178x^3+81x^2+140x+129$
• $y^2=173x^6+21x^5+93x^4+72x^3+145x^2+53x+94$
• $y^2=87x^6+3x^5+119x^4+66x^3+140x^2+38x+45$
• $y^2=180x^6+158x^5+12x^4+173x^3+98x^2+34x+75$
• $y^2=147x^6+156x^5+68x^4+49x^3+175x^2+90x+189$
• $y^2=181x^6+123x^5+131x^4+116x^3+90x^2+174x+84$
• $y^2=162x^6+154x^5+10x^4+103x^3+133x^2+2x+20$

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 4.0.383725.4.

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.bv_bjn	$2$	(not in LMFDB)