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

• Label: 2.193.abw_bkt
• 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:	$1 - 48 x + 955 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0914626496846$, $\pm0.220975467824$
Angle rank:	$2$ (numerical)
Number field:	4.0.15360912.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28893$	$1372908681$	$51676334413524$	$1925177234878552761$	$71709130057453807360773$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36856$	$7188194$	$1387527124$	$267786025106$	$51682550223526$	$9974730381908690$	$1925122952696370148$	$371548729907588680418$	$71708904873371922778696$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=40x^6+115x^5+24x^4+141x^3+186x^2+12x+70$
• $y^2=106x^6+77x^5+38x^4+22x^3+127x^2+141x+132$
• $y^2=2x^6+118x^5+32x^4+3x^3+19x^2+96x+149$
• $y^2=102x^6+17x^5+129x^4+165x^3+85x^2+190x+140$
• $y^2=91x^6+154x^5+6x^4+15x^3+165x^2+59x+54$
• $y^2=102x^6+144x^5+157x^4+16x^3+171x^2+44x+7$
• $y^2=150x^6+43x^5+86x^4+54x^3+31x^2+63x+30$
• $y^2=152x^6+65x^5+35x^4+113x^3+91x^2+130x+135$
• $y^2=111x^6+84x^5+25x^4+175x^3+134x^2+162x+146$
• $y^2=10x^6+110x^5+136x^4+46x^3+156x^2+125x+66$
• $y^2=88x^6+70x^5+165x^4+15x^3+136x^2+109x+150$
• $y^2=138x^6+51x^5+181x^4+101x^3+141x^2+111x+13$
• $y^2=111x^6+83x^5+6x^4+169x^3+156x^2+73x+130$
• $y^2=10x^6+14x^5+127x^4+113x^3+141x^2+143x+37$
• $y^2=69x^6+22x^5+151x^4+133x^3+104x^2+65x+16$
• $y^2=17x^6+130x^5+189x^4+186x^3+126x^2+107x+65$
• $y^2=187x^6+47x^5+12x^4+89x^3+52x^2+188x+141$
• $y^2=93x^6+144x^5+185x^4+149x^3+147x^2+10x+119$
• $y^2=45x^6+56x^5+143x^4+30x^3+107x^2+68x+10$
• $y^2=66x^6+178x^5+41x^4+106x^3+146x^2+47x+134$
• $y^2=51x^6+14x^5+101x^4+64x^3+181x^2+122x+157$
• $y^2=44x^6+132x^5+x^4+39x^3+138x^2+105x+18$
• $y^2=61x^6+123x^5+65x^4+62x^3+65x^2+80x+153$
• $y^2=81x^6+45x^5+151x^4+170x^3+24x^2+97x+44$

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 4.0.15360912.1.

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_bkt	$2$	(not in LMFDB)