Abelian variety isogeny class 2.193.aby_bmu over $\F_{193}$

• Label: 2.193.aby_bmu
• Base field: $\F_{193}$
• 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:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$1 - 50 x + 1008 x^{2} - 9650 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0879067867460$, $\pm0.184056049243$
Angle rank:	$2$ (numerical)
Number field:	4.0.1905984.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28558$	$1369584564$	$51662781846286$	$1925146358155782096$	$71709121043208505833118$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36766$	$7186308$	$1387504870$	$267785991444$	$51682555399822$	$9974730520036608$	$1925122954812823294$	$371548729925709694944$	$71708904873306540829486$

Jacobians and polarizations

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

• $y^2=159x^6+47x^5+133x^4+143x^3+12x^2+62x+18$
• $y^2=116x^6+189x^5+52x^4+52x^3+133x^2+182x+32$
• $y^2=45x^6+60x^5+58x^4+106x^3+22x^2+39x+116$
• $y^2=49x^6+88x^5+142x^4+3x^3+15x^2+124x+90$
• $y^2=115x^6+106x^5+125x^4+97x^3+150x^2+54x+96$
• $y^2=76x^6+42x^5+27x^4+46x^3+76x^2+77x+157$
• $y^2=150x^6+187x^5+19x^4+38x^3+97x^2+130x+14$
• $y^2=71x^6+61x^5+122x^4+164x^3+150x^2+127x+11$
• $y^2=79x^6+21x^5+160x^4+127x^3+115x^2+93x+133$
• $y^2=89x^6+120x^5+118x^4+153x^3+28x^2+186x+93$
• $y^2=122x^6+86x^5+157x^4+13x^3+90x^2+x+15$
• $y^2=102x^6+143x^5+123x^4+60x^3+92x^2+142x+37$
• $y^2=101x^6+144x^4+53x^3+98x^2+103x+104$
• $y^2=51x^6+191x^5+x^4+141x^3+26x^2+159x+40$
• $y^2=184x^6+81x^5+41x^4+121x^3+148x^2+26x+39$
• $y^2=41x^6+22x^5+32x^4+47x^3+160x^2+104x+79$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The endomorphism algebra of this simple isogeny class is 4.0.1905984.1.

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
2.193.by_bmu	$2$	(not in LMFDB)