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

• Label: 2.193.abw_bkx
• 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:	$1 - 48 x + 959 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.123125767166$, $\pm0.204067046721$
Angle rank:	$2$ (numerical)
Number field:	4.0.4368528.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28897$	$1373214337$	$51680480518084$	$1925207140031458569$	$71709279931981031712097$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36864$	$7188770$	$1387548676$	$267786584786$	$51682561301382$	$9974730551751314$	$1925122954568540164$	$371548729916127887906$	$71708904873148067126784$

Jacobians and polarizations

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

• $y^2=141x^6+124x^5+133x^4+178x^3+130x^2+164x+133$
• $y^2=131x^6+117x^5+192x^4+6x^3+77x^2+103x+35$
• $y^2=15x^6+37x^5+77x^4+147x^3+109x^2+183x+139$
• $y^2=134x^6+166x^5+8x^4+56x^3+177x^2+37x+18$
• $y^2=41x^6+61x^5+88x^4+85x^3+65x^2+23x+146$
• $y^2=30x^6+99x^5+141x^4+123x^3+150x^2+146x+84$
• $y^2=152x^6+106x^5+64x^4+121x^3+179x^2+83x+84$
• $y^2=37x^6+138x^5+100x^4+111x^3+160x^2+122x+33$
• $y^2=15x^6+167x^5+139x^4+91x^3+70x^2+177x+56$
• $y^2=8x^6+140x^5+98x^4+49x^3+87x^2+9x+97$
• $y^2=68x^6+48x^5+157x^4+167x^3+110x^2+18x+30$
• $y^2=53x^6+74x^5+93x^4+103x^3+84x^2+161x+161$
• $y^2=24x^6+22x^5+130x^4+55x^3+11x^2+6x+190$
• $y^2=108x^6+154x^5+45x^4+82x^3+114x^2+71x+128$
• $y^2=132x^6+61x^5+16x^4+23x^3+110x^2+102x+63$
• $y^2=146x^6+16x^5+51x^4+38x^3+110x^2+148x+92$

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 4.0.4368528.2.

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_bkx	$2$	(not in LMFDB)