Abelian variety isogeny class 2.199.abw_bkx over $\F_{199}$

• Label: 2.199.abw_bkx
• Base field: $\F_{199}$
• 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:	$\F_{199}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 959 x^{2} - 9552 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.0495023584196$, $\pm0.247161933256$
Angle rank:	$2$ (numerical)
Number field:	4.0.26874000.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30961$	$1553034721$	$62094758540836$	$2459397377579792265$	$97393686182777253789121$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$152$	$39216$	$7879448$	$1568253988$	$312079629272$	$62103832058166$	$12358664028954248$	$2459374187418158788$	$489415464077841404552$	$97393677359629707530256$

Jacobians and polarizations

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

• $y^2=192x^6+111x^5+101x^4+7x^3+153x^2+159x+178$
• $y^2=195x^6+67x^5+9x^4+134x^3+34x^2+11x+73$
• $y^2=166x^6+10x^5+69x^4+65x^3+62x^2+167x+163$
• $y^2=30x^6+66x^5+123x^4+21x^3+11x^2+181x+51$
• $y^2=42x^6+192x^5+70x^4+35x^3+76x^2+52x+6$
• $y^2=157x^6+132x^5+39x^4+117x^3+88x^2+82x+170$
• $y^2=141x^6+196x^5+139x^4+181x^3+133x^2+2x+61$
• $y^2=84x^6+91x^5+100x^4+45x^3+84x^2+103x+113$
• $y^2=186x^6+124x^5+40x^4+88x^3+40x^2+59x+90$
• $y^2=143x^6+106x^5+170x^4+129x^3+57x^2+147x+33$
• $y^2=147x^6+76x^5+90x^4+74x^3+70x^2+62x+69$
• $y^2=167x^6+166x^5+94x^4+129x^3+58x^2+107x+19$
• $y^2=26x^6+82x^5+170x^4+152x^3+117x^2+166x+125$
• $y^2=21x^6+64x^5+175x^4+25x^3+187x^2+31x+49$
• $y^2=139x^6+34x^5+131x^4+129x^3+99x^2+108x+54$
• $y^2=113x^6+25x^5+20x^4+124x^3+154x^2+134x+75$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{199}$.

Endomorphism algebra over $\F_{199}$

The endomorphism algebra of this simple isogeny class is 4.0.26874000.1.

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
2.199.bw_bkx	$2$	(not in LMFDB)