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

• Label: 2.193.aby_bmt
• 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:	$( 1 - 27 x + 193 x^{2} )( 1 - 23 x + 193 x^{2} )$
	$1 - 50 x + 1007 x^{2} - 9650 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0758389534121$, $\pm0.189598946136$
Angle rank:	$2$ (numerical)
Jacobians:	$26$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28557$	$1369508049$	$51661702001664$	$1925138074205929401$	$71709075653424180319557$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36764$	$7186158$	$1387498900$	$267785821944$	$51682551580478$	$9974730448540008$	$1925122953685624804$	$371548729910997914094$	$71708904873160259068364$

Jacobians and polarizations

This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=82x^6+11x^5+117x^4+64x^3+45x^2+77x+102$
• $y^2=166x^6+24x^5+186x^4+141x^3+128x^2+138x+57$
• $y^2=83x^6+17x^5+43x^4+99x^3+109x^2+106x+95$
• $y^2=20x^6+151x^5+25x^4+59x^3+130x^2+169x+87$
• $y^2=40x^6+48x^5+165x^4+125x^3+126x^2+7x+22$
• $y^2=37x^6+125x^5+66x^4+62x^3+79x^2+179x+101$
• $y^2=46x^6+88x^5+140x^4+161x^3+32x^2+22x+170$
• $y^2=28x^6+161x^5+154x^4+120x^3+106x^2+92x+6$
• $y^2=41x^6+3x^5+61x^4+69x^3+104x^2+172x+115$
• $y^2=7x^6+115x^5+31x^4+30x^3+78x^2+180x+157$
• $y^2=42x^6+118x^5+44x^4+100x^3+50x^2+31x+43$
• $y^2=162x^6+105x^5+87x^4+50x^3+135x^2+111x+145$
• $y^2=16x^6+129x^5+119x^4+25x^3+137x^2+63x+104$
• $y^2=142x^6+103x^5+80x^4+164x^3+141x^2+44x+70$
• $y^2=20x^6+115x^5+122x^4+17x^3+52x^2+77x+118$
• $y^2=67x^6+138x^5+60x^4+56x^3+58x^2+192x+42$
• $y^2=148x^6+43x^5+129x^4+11x^3+59x^2+7x+5$
• $y^2=102x^6+68x^5+80x^4+23x^3+166x+47$
• $y^2=19x^6+49x^5+34x^4+148x^3+69x^2+175x+22$
• $y^2=13x^6+80x^5+69x^4+68x^3+175x^2+2x+120$
• $y^2=179x^6+172x^5+82x^4+192x^3+156x^2+62x+121$
• $y^2=159x^6+27x^5+111x^4+44x^3+111x^2+27x+159$
• $y^2=84x^6+82x^5+33x^4+121x^3+28x^2+63x+181$
• $y^2=109x^6+152x^5+80x^4+158x^3+10x^2+106x+130$
• $y^2=60x^6+115x^5+112x^4+151x^3+169x^2+152x+182$
• $y^2=13x^6+166x^5+192x^4+187x^3+150x^2+152x+1$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{193}$

The isogeny class factors as 1.193.abb $\times$ 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.abb : \(\Q(\sqrt{-43}) \).
• 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.ae_ajb	$2$	(not in LMFDB)
2.193.e_ajb	$2$	(not in LMFDB)
2.193.by_bmt	$2$	(not in LMFDB)
2.193.abd_qy	$3$	(not in LMFDB)
2.193.ac_ald	$3$	(not in LMFDB)