Abelian variety isogeny class 3.16.av_hn_abnb over $\F_{2^{4}}$

• Label: 3.16.av_hn_abnb
• Base field: $\F_{2^{4}}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{2^{4}}$
Dimension:	$3$
L-polynomial:	$( 1 - 7 x + 16 x^{2} )^{3}$
	$1 - 21 x + 195 x^{2} - 1015 x^{3} + 3120 x^{4} - 5376 x^{5} + 4096 x^{6}$
Frobenius angles:	$\pm0.160861246510$, $\pm0.160861246510$, $\pm0.160861246510$
Angle rank:	$1$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1000$	$13824000$	$68417929000$	$284371070976000$	$1158452071890625000$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$-4$	$206$	$4076$	$66206$	$1053596$	$16801646$	$268526156$	$4295211326$	$68719733756$	$1099509522446$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{4}}$.

Endomorphism algebra over $\F_{2^{4}}$

The isogeny class factors as 1.16.ah^3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-15}) \)$)$

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
3.16.ah_ab_ep	$2$	(not in LMFDB)
3.16.h_ab_aep	$2$	(not in LMFDB)
3.16.v_hn_bnb	$2$	(not in LMFDB)
3.16.a_a_ah	$3$	(not in LMFDB)