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

• Label: 2.191.aby_bmt
• 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:	$( 1 - 25 x + 191 x^{2} )^{2}$
	$1 - 50 x + 1007 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.140267993779$, $\pm0.140267993779$
Angle rank:	$1$ (numerical)
Jacobians:	$21$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27889$	$1313265121$	$48533125431184$	$1771234321111425625$	$64615351242614110697929$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$142$	$35996$	$6965272$	$1330891188$	$254196094202$	$48551250764126$	$9273284602641782$	$1771197290588526628$	$338298681609528711112$	$64615048178184553182956$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=178x^6+43x^5+121x^4+47x^3+37x^2+71x+93$
• $y^2=96x^6+68x^5+64x^4+163x^3+7x^2+68x+11$
• $y^2=160x^6+59x^5+129x^4+110x^3+135x^2+185x+49$
• $y^2=50x^6+52x^5+25x^4+172x^3+25x^2+52x+50$
• $y^2=58x^6+9x^5+48x^4+78x^3+40x^2+74x+171$
• $y^2=91x^6+176x^5+6x^4+64x^3+6x^2+176x+91$
• $y^2=123x^6+125x^5+63x^4+96x^3+63x^2+125x+123$
• $y^2=169x^6+150x^5+97x^4+67x^3+97x^2+150x+169$
• $y^2=146x^6+151x^5+163x^4+182x^3+26x^2+12x+5$
• $y^2=56x^6+139x^5+144x^4+158x^3+144x^2+139x+56$
• $y^2=155x^6+70x^5+139x^4+164x^3+139x^2+70x+155$
• $y^2=137x^6+128x^5+172x^4+52x^3+172x^2+128x+137$
• $y^2=164x^6+104x^5+49x^4+100x^3+79x+153$
• $y^2=x^6+92x^5+150x^4+77x^3+145x^2+167x+105$
• $y^2=33x^6+123x^5+62x^4+189x^3+62x^2+123x+33$
• $y^2=178x^6+173x^5+87x^4+48x^3+3x^2+38x+112$
• $y^2=170x^6+190x^5+16x^4+71x^3+16x^2+190x+170$
• $y^2=84x^6+22x^5+35x^4+10x^3+35x^2+22x+84$
• $y^2=167x^6+134x^5+18x^4+14x^3+18x^2+134x+167$
• $y^2=127x^6+174x^5+108x^4+139x^3+108x^2+174x+127$
• $y^2=179x^6+4x^5+102x^4+33x^3+47x^2+107x+149$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.az^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-139}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.191.a_ajj	$2$	(not in LMFDB)
2.191.by_bmt	$2$	(not in LMFDB)
2.191.z_qs	$3$	(not in LMFDB)