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

• Label: 2.193.abw_bky
• 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:	$1 - 48 x + 960 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.132444567603$, $\pm0.197898328146$
Angle rank:	$2$ (numerical)
Number field:	4.0.2113792.1
Galois group:	$D_{4}$
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28898$	$1373290756$	$51681517058594$	$1925214602462699536$	$71709317079284242891298$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36866$	$7188914$	$1387554054$	$267786723506$	$51682563995906$	$9974730590974610$	$1925122954928540158$	$371548729915322666258$	$71708904873025163218946$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=88x^6+105x^5+9x^4+147x^3+50x^2+36x+71$
• $y^2=142x^6+112x^5+156x^4+46x^3+140x^2+151x+95$
• $y^2=138x^6+63x^5+34x^4+24x^3+31x^2+113x+71$
• $y^2=143x^6+10x^5+91x^4+163x^3+44x^2+13x+185$
• $y^2=15x^6+81x^5+90x^4+8x^3+124x^2+8x+111$
• $y^2=97x^6+111x^5+40x^4+188x^3+14x^2+83x+144$
• $y^2=175x^6+87x^5+165x^4+32x^3+129x^2+145x+86$
• $y^2=71x^6+47x^5+25x^4+166x^3+186x^2+189x+35$
• $y^2=135x^6+159x^5+9x^4+130x^3+108x^2+189x+153$
• $y^2=70x^6+156x^5+43x^4+110x^3+7x^2+22x+158$
• $y^2=65x^6+101x^5+101x^4+16x^3+39x^2+169x+125$
• $y^2=54x^6+107x^5+49x^4+2x^3+179x^2+37x+168$
• $y^2=29x^6+129x^5+147x^4+183x^3+60x^2+87x+185$
• $y^2=25x^6+109x^5+89x^4+146x^3+74x^2+80x+97$
• $y^2=12x^6+145x^5+49x^4+80x^3+54x^2+172x+115$
• $y^2=176x^6+185x^5+181x^4+190x^3+142x^2+19x+149$
• $y^2=97x^6+81x^5+177x^4+170x^3+104x^2+185x+36$
• $y^2=121x^6+85x^5+101x^4+49x^3+85x^2+191x+51$
• $y^2=142x^6+132x^5+77x^4+138x^3+115x^2+93x+89$
• $y^2=5x^6+179x^5+131x^4+192x^3+109x^2+54x+134$

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 4.0.2113792.1.

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.bw_bky	$2$	(not in LMFDB)