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

• Label: 2.199.abx_bmh
• Base field: $\F_{199}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 49 x + 995 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.117818821654$, $\pm0.202443120192$
Angle rank:	$2$ (numerical)
Number field:	4.0.4943757.1
Galois group:	$D_{4}$
Jacobians:	$16$

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30797$	$1552076409$	$62098831784483$	$2459465680592592477$	$97394122110296462549072$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$151$	$39191$	$7879963$	$1568297539$	$312081026116$	$62103862448795$	$12358664525890561$	$2459374193488206835$	$489415464125017642849$	$97393677359601610254686$

Jacobians and polarizations

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

• $y^2=128x^6+91x^5+11x^4+8x^3+129x^2+165x+50$
• $y^2=24x^6+171x^5+102x^4+10x^3+195x^2+80x+196$
• $y^2=16x^6+131x^5+29x^4+184x^3+22x^2+191x+19$
• $y^2=48x^6+64x^5+125x^4+192x^3+121x^2+144x+46$
• $y^2=71x^6+188x^5+187x^4+40x^3+167x^2+29x+183$
• $y^2=144x^6+150x^5+72x^4+49x^3+84x^2+30x+75$
• $y^2=121x^6+63x^5+125x^4+82x^3+161x^2+72x+29$
• $y^2=19x^6+27x^5+131x^4+194x^3+5x^2+82x+109$
• $y^2=146x^6+105x^5+44x^4+12x^3+153x^2+53x+62$
• $y^2=54x^6+3x^5+6x^4+112x^3+194x^2+29x+149$
• $y^2=91x^6+34x^5+157x^4+68x^3+120x^2+154x+156$
• $y^2=52x^6+69x^5+130x^4+44x^3+132x^2+119x+144$
• $y^2=175x^6+185x^5+116x^4+48x^3+175x^2+44x+93$
• $y^2=107x^6+168x^5+102x^4+151x^3+42x^2+69x+29$
• $y^2=71x^6+173x^5+83x^4+85x^3+18x^2+26x+107$
• $y^2=119x^6+46x^5+10x^4+114x^3+34x^2+7x+138$

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 4.0.4943757.1.

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.bx_bmh	$2$	(not in LMFDB)