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

• Label: 2.193.abx_blw
• Base field: $\F_{193}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 193 x^{2} )( 1 - 23 x + 193 x^{2} )$
	$1 - 49 x + 984 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.114714697559$, $\pm0.189598946136$
Angle rank:	$2$ (numerical)
Jacobians:	$27$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28728$	$1371474720$	$51672688639488$	$1925184624854198400$	$71709241820388123337848$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36817$	$7187686$	$1387532449$	$267786442465$	$51682561622494$	$9974730591896257$	$1925122955455435201$	$371548729928432261158$	$71708904873251061767857$

Jacobians and polarizations

This isogeny class contains the Jacobians of 27 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=20x^6+103x^5+53x^4+3x^3+149x^2+7x+168$
• $y^2=19x^6+34x^5+76x^4+52x^3+185x^2+43x+165$
• $y^2=75x^6+13x^5+57x^4+66x^3+54x^2+38x+39$
• $y^2=66x^6+144x^5+185x^4+70x^3+149x^2+25x+34$
• $y^2=132x^6+87x^5+183x^4+99x^3+19x^2+111x+39$
• $y^2=171x^6+147x^5+35x^4+127x^3+90x^2+149x+153$
• $y^2=89x^6+57x^5+40x^4+132x^3+28x^2+115x+106$
• $y^2=152x^6+17x^5+66x^4+96x^3+97x^2+73x+26$
• $y^2=129x^6+82x^5+78x^4+50x^3+172x^2+23x+90$
• $y^2=111x^6+53x^5+144x^4+34x^3+147x^2+192x+127$
• $y^2=118x^6+57x^5+119x^4+45x^3+64x^2+88x+11$
• $y^2=132x^6+123x^5+159x^4+14x^3+172x^2+50x+178$
• $y^2=92x^6+76x^5+37x^4+156x^3+60x^2+20x+30$
• $y^2=114x^6+74x^5+44x^4+123x^3+116x^2+47x+61$
• $y^2=24x^6+173x^5+188x^4+41x^3+97x^2+30x+103$
• $y^2=102x^6+17x^5+140x^4+100x^3+74x^2+54x+98$
• $y^2=141x^6+15x^5+96x^4+167x^3+15x^2+25x+65$
• $y^2=146x^6+42x^5+19x^4+45x^3+52x^2+91x+2$
• $y^2=70x^6+67x^5+77x^4+97x^3+138x^2+136x+36$
• $y^2=47x^6+189x^5+5x^4+137x^3+124x^2+156x+111$
• $y^2=5x^6+28x^5+157x^4+142x^3+53x^2+192x+80$
• $y^2=162x^6+167x^5+185x^4+105x^3+115x^2+56x+29$
• $y^2=133x^6+132x^5+16x^4+128x^3+16x^2+19x+170$
• $y^2=38x^6+134x^5+128x^4+157x^3+57x^2+110x+121$
• $y^2=190x^6+66x^5+176x^4+142x^3+141x^2+6x+25$
• $y^2=20x^6+11x^5+182x^4+6x^3+143x^2+61x+68$
• $y^2=124x^6+40x^5+190x^4+153x^3+86x^2+107x+45$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{193}$

The isogeny class factors as 1.193.aba $\times$ 1.193.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.193.aba : \(\Q(\sqrt{-6}) \).
• 1.193.ax : \(\Q(\sqrt{-3}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.193.ad_aie	$2$	(not in LMFDB)
2.193.d_aie	$2$	(not in LMFDB)
2.193.bx_blw	$2$	(not in LMFDB)
2.193.abc_qw	$3$	(not in LMFDB)
2.193.ab_ake	$3$	(not in LMFDB)