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

• Label: 2.193.abz_bnt
• 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:	$1 - 51 x + 1033 x^{2} - 9843 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0593833791648$, $\pm0.174852758199$
Angle rank:	$2$ (numerical)
Number field:	4.0.11661.1
Galois group:	$D_{4}$
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28389$	$1367696853$	$51652855050525$	$1925107659024551109$	$71708995610628624309504$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$143$	$36715$	$7184927$	$1387476979$	$267785523038$	$51682548483835$	$9974730426019271$	$1925122953569111779$	$371548729908683130791$	$71708904873057590237950$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=41x^6+4x^5+169x^4+163x^3+99x^2+34x+153$
• $y^2=175x^6+6x^5+77x^4+92x^3+73x^2+87x+189$
• $y^2=125x^6+97x^5+148x^4+48x^3+43x^2+83x+58$
• $y^2=141x^6+188x^5+117x^4+30x^3+119x^2+34x+31$
• $y^2=114x^6+107x^5+152x^4+104x^3+189x^2+189x+9$
• $y^2=104x^6+15x^5+190x^4+97x^3+9x^2+158x+167$
• $y^2=157x^6+119x^5+123x^4+99x^3+190x^2+52x+95$
• $y^2=21x^6+77x^5+117x^4+158x^3+126x^2+10x+107$
• $y^2=37x^6+176x^5+122x^4+127x^3+124x^2+25x+182$
• $y^2=47x^6+140x^5+84x^4+180x^3+55x^2+31x+52$
• $y^2=5x^6+111x^5+120x^4+101x^3+133x^2+140x+67$
• $y^2=47x^6+170x^5+28x^4+144x^3+87x^2+152x+177$
• $y^2=44x^6+119x^5+11x^4+41x^3+9x^2+173x+181$
• $y^2=118x^6+59x^5+58x^4+147x^3+124x^2+137x+142$
• $y^2=115x^6+62x^5+60x^4+85x^3+26x^2+57x+169$
• $y^2=132x^6+10x^5+70x^4+26x^3+136x^2+120x+187$
• $y^2=123x^6+54x^5+101x^4+155x^3+137x^2+51x+5$
• $y^2=112x^6+187x^5+3x^4+152x^3+135x^2+132x+47$

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 4.0.11661.1.

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.bz_bnt	$2$	(not in LMFDB)