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

• Label: 2.191.abx_blt
• 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:	$1 - 49 x + 981 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.122524293102$, $\pm0.179046122411$
Angle rank:	$2$ (numerical)
Number field:	4.0.585125.1
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28055$	$1314965905$	$48540654699605$	$1771255261948841405$	$64615379546177676250000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$143$	$36043$	$6966353$	$1330906923$	$254196205548$	$48551249214343$	$9273284526492143$	$1771197288870081603$	$338298681581845835573$	$64615048177862676323598$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=13x^6+158x^5+71x^4+170x^3+65x^2+18x+141$
• $y^2=124x^6+37x^5+136x^4+x^3+95x^2+103x+190$
• $y^2=89x^6+8x^5+124x^4+100x^3+59x^2+174x+141$
• $y^2=165x^6+49x^5+27x^4+87x^3+100x^2+44x+184$
• $y^2=103x^6+142x^5+90x^4+158x^3+123x^2+82x+88$
• $y^2=115x^6+49x^5+81x^4+115x^3+12x^2+106x+50$
• $y^2=88x^6+178x^5+143x^4+187x^3+57x^2+145x+55$
• $y^2=47x^6+151x^5+93x^4+16x^3+86x^2+44x+38$
• $y^2=13x^6+190x^5+181x^4+88x^3+168x^2+134x+31$
• $y^2=144x^6+82x^5+18x^4+135x^3+116x^2+68x+126$
• $y^2=161x^6+73x^5+38x^4+41x^3+30x^2+51x+38$
• $y^2=182x^6+170x^5+17x^4+72x^3+160x^2+120x+41$
• $y^2=22x^6+2x^5+33x^4+135x^3+79x+161$
• $y^2=7x^6+28x^5+82x^4+91x^3+73x^2+26x+79$
• $y^2=144x^6+8x^5+170x^4+153x^3+141x^2+91x+167$
• $y^2=39x^6+19x^5+43x^4+21x^3+116x^2+163x+174$

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 4.0.585125.1.

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_blt	$2$	(not in LMFDB)