Abelian variety isogeny class 2.163.abs_bex over $\F_{163}$

• Label: 2.163.abs_bex
• Base field: $\F_{163}$
• 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:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$1 - 44 x + 803 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0842188003801$, $\pm0.226190889167$
Angle rank:	$2$ (numerical)
Number field:	4.0.9697296.3
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20157$	$697210473$	$18752322930516$	$498328865957506329$	$13239688362053184916557$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$120$	$26240$	$4330044$	$705936484$	$115064072400$	$18755373480590$	$3057125243288880$	$498311413884553924$	$81224760529002786372$	$13239635967064055307200$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=66x^6+151x^5+124x^4+64x^3+146x^2+71x+61$
• $y^2=7x^6+102x^5+82x^4+146x^3+144x^2+72x+76$
• $y^2=52x^6+63x^5+71x^4+89x^3+131x^2+133x+55$
• $y^2=134x^6+120x^5+61x^4+42x^3+139x^2+79x+140$
• $y^2=49x^6+57x^5+112x^4+9x^3+47x^2+142x+102$
• $y^2=30x^6+124x^5+162x^4+37x^3+57x^2+151x+57$
• $y^2=18x^6+5x^5+47x^4+55x^3+126x^2+76x+152$
• $y^2=17x^6+33x^5+107x^4+86x^3+24x^2+86x+120$
• $y^2=8x^6+9x^5+106x^4+77x^3+45x^2+145x+39$
• $y^2=134x^6+93x^5+55x^4+158x^3+137x^2+6x+74$
• $y^2=92x^6+136x^5+119x^4+57x^3+2x^2+156x+97$
• $y^2=33x^6+157x^5+90x^4+8x^3+124x^2+156x+27$
• $y^2=134x^6+94x^5+154x^4+21x^3+145x^2+86x+105$
• $y^2=115x^6+19x^5+74x^4+143x^3+59x^2+66x+82$
• $y^2=129x^6+25x^5+111x^4+108x^3+64x^2+107x+138$
• $y^2=16x^6+46x^5+78x^4+75x^3+57x^2+88x+45$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The endomorphism algebra of this simple isogeny class is 4.0.9697296.3.

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
2.163.bs_bex	$2$	(not in LMFDB)