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

• Label: 2.193.abw_bkp
• 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:	$1 - 48 x + 951 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0585217950236$, $\pm0.232730388834$
Angle rank:	$2$ (numerical)
Number field:	4.0.17193616.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28889$	$1372603057$	$51672188400644$	$1925147241039838249$	$71708978126421636040649$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36848$	$7187618$	$1387505508$	$267785457746$	$51682538665478$	$9974730191250194$	$1925122950124314436$	$371548729879729686434$	$71708904873144091049168$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=102x^6+75x^5+192x^4+148x^3+174x^2+29x+121$
• $y^2=177x^6+102x^4+53x^3+170x^2+91x+115$
• $y^2=177x^6+23x^5+86x^4+70x^3+63x^2+21x+22$
• $y^2=82x^6+52x^5+151x^4+25x^3+122x^2+167x+160$
• $y^2=156x^6+135x^5+137x^4+5x^3+13x^2+185x+175$
• $y^2=72x^6+3x^5+150x^4+188x^3+12x^2+108x+168$
• $y^2=180x^6+76x^5+53x^4+89x^3+130x^2+120x+42$
• $y^2=40x^6+181x^5+101x^4+169x^3+60x^2+121x+116$
• $y^2=130x^6+66x^5+15x^4+144x^3+188x^2+148x+125$
• $y^2=133x^6+134x^5+189x^4+36x^3+19x^2+98x+146$
• $y^2=152x^6+89x^5+124x^4+114x^3+192x^2+92x+168$
• $y^2=80x^6+87x^5+158x^4+100x^3+129x^2+192x+175$
• $y^2=47x^6+180x^5+129x^4+115x^3+166x^2+150x+26$
• $y^2=113x^6+49x^5+137x^4+64x^3+83x^2+21x+10$

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 4.0.17193616.1.

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_bkp	$2$	(not in LMFDB)