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

• Label: 2.191.abw_bkn
• 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:	$( 1 - 27 x + 191 x^{2} )( 1 - 21 x + 191 x^{2} )$
	$1 - 48 x + 949 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0686610702072$, $\pm0.225319681555$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28215$	$1316145105$	$48541194797040$	$1771226609260596345$	$64615163346536461275375$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36076$	$6966432$	$1330885396$	$254195355024$	$48551228719198$	$9273284160084144$	$1771197283896842596$	$338298681536249667552$	$64615048177803910314076$

Jacobians and polarizations

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

• $y^2=28x^6+190x^5+144x^4+68x^3+48x^2+106x+93$
• $y^2=11x^6+151x^5+26x^4+4x^3+175x^2+74x+119$
• $y^2=65x^6+108x^5+177x^4+49x^3+32x^2+163x+33$
• $y^2=16x^6+138x^5+110x^4+3x^3+111x^2+43x+92$
• $y^2=181x^6+60x^5+143x^4+15x^3+186x^2+143x+163$
• $y^2=115x^6+129x^5+181x^4+5x^3+112x^2+33x+27$
• $y^2=63x^6+123x^5+105x^4+96x^3+109x^2+49x+86$
• $y^2=76x^6+163x^5+11x^4+35x^3+66x^2+15x+155$
• $y^2=9x^6+171x^5+183x^4+154x^3+185x^2+132x+156$
• $y^2=105x^6+65x^5+23x^4+11x^3+176x^2+122x+118$
• $y^2=23x^6+175x^5+120x^4+44x^3+161x^2+45x+182$
• $y^2=131x^6+13x^5+153x^4+113x^3+6x^2+49x+62$
• $y^2=73x^6+65x^5+144x^4+47x^3+102x^2+43x+47$
• $y^2=164x^6+160x^5+144x^4+63x^3+92x^2+4x+70$
• $y^2=178x^6+58x^5+37x^4+3x^3+33x^2+129x+67$
• $y^2=169x^6+162x^5+139x^4+98x^3+182x^2+170x+36$
• $y^2=135x^6+104x^5+92x^4+96x^3+25x^2+113x+69$
• $y^2=167x^6+85x^5+154x^4+171x^3+179x^2+174x+23$
• $y^2=28x^6+6x^5+156x^4+165x^3+117x^2+75x+167$
• $y^2=162x^6+174x^5+147x^4+91x^3+61x^2+64x+14$
• and

• $y^2=135x^6+138x^5+27x^4+72x^3+97x^2+103x+153$
• $y^2=127x^6+7x^5+177x^4+94x^3+134x^2+41x+185$
• $y^2=93x^6+187x^5+132x^4+72x^3+69x^2+161x+124$
• $y^2=95x^6+173x^5+10x^4+38x^3+162x^2+74x+167$
• $y^2=108x^6+160x^5+107x^4+117x^3+7x^2+69x+88$
• $y^2=181x^6+79x^5+177x^4+172x^3+120x^2+39x+167$
• $y^2=107x^6+168x^5+70x^4+164x^3+31x^2+134x+25$
• $y^2=63x^6+6x^5+54x^4+69x^3+7x^2+82x+86$
• $y^2=117x^6+190x^5+184x^4+76x^3+70x^2+97x+63$
• $y^2=62x^6+143x^5+123x^4+9x^3+185x^2+142x+41$
• $y^2=54x^6+161x^5+133x^4+99x^3+18x^2+152x+23$
• $y^2=13x^6+41x^5+19x^4+60x^3+165x^2+190x+48$
• $y^2=114x^6+27x^5+138x^4+135x^3+x^2+153x+168$
• $y^2=80x^6+107x^5+18x^4+147x^3+2x^2+75x+26$
• $y^2=24x^6+95x^5+63x^4+139x^3+62x^2+44x+10$
• $y^2=11x^6+163x^5+66x^4+17x^3+113x^2+86x+90$
• $y^2=47x^6+3x^5+37x^4+69x^3+105x^2+x+189$
• $y^2=190x^6+27x^5+32x^4+85x^3+48x^2+13x+116$
• $y^2=99x^6+149x^5+11x^4+42x^3+161x^2+158x+88$
• $y^2=60x^6+173x^5+92x^4+178x^3+163x^2+117x+17$
• $y^2=26x^6+177x^5+22x^4+3x^3+98x^2+19x+183$
• $y^2=171x^6+180x^5+140x^4+65x^3+132x^2+87x+93$
• $y^2=142x^6+185x^5+61x^4+16x^3+178x^2+126x+122$
• $y^2=41x^6+38x^5+61x^4+130x^3+64x^2+124x+7$
• $y^2=6x^6+158x^5+134x^4+4x^3+86x^2+15x+69$
• $y^2=131x^6+30x^5+45x^4+98x^3+117x^2+71x+168$
• $y^2=146x^6+10x^5+25x^4+158x^3+x^2+181x+184$
• $y^2=32x^6+87x^5+58x^4+75x^3+94x^2+187x+161$
• $y^2=71x^6+125x^5+70x^4+57x^3+2x^2+86x+112$
• $y^2=95x^6+140x^5+28x^4+27x^3+74x^2+132x+188$
• $y^2=46x^6+98x^5+170x^4+6x^3+171x^2+43x+153$
• $y^2=140x^6+126x^5+109x^4+120x^3+129x^2+151x+87$
• $y^2=29x^6+53x^5+182x^4+31x^3+157x^2+82x+73$
• $y^2=86x^6+8x^5+90x^4+129x^3+17x^2+108x+162$
• $y^2=40x^6+130x^5+45x^4+120x^3+36x^2+45x+158$
• $y^2=47x^6+175x^5+179x^4+48x^3+21x^2+91x+143$

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.av 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.av : \(\Q(\sqrt{-323}) \).

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.ag_ahd	$2$	(not in LMFDB)
2.191.g_ahd	$2$	(not in LMFDB)
2.191.bw_bkn	$2$	(not in LMFDB)