Abelian variety isogeny class 3.7.aj_bq_afd over $\F_{7}$

• Label: 3.7.aj_bq_afd
• Base field: $\F_{7}$
• Dimension: $3$
• $p$-rank: $1$
• Ordinary: no
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{7}$
Dimension:	$3$
L-polynomial:	$1 - 9 x + 42 x^{2} - 133 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:	$\pm0.0337411547966$, $\pm0.282571984656$, $\pm0.476016355688$
Angle rank:	$3$ (numerical)
Number field:	6.0.1714608.1
Galois group:	$D_{6}$
Isomorphism classes:	3

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

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$97$	$122511$	$41003452$	$13303346979$	$4678048479367$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$-1$	$53$	$350$	$2309$	$16559$	$117320$	$821309$	$5754389$	$40340006$	$282512033$

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 $\F_{7}$.

Endomorphism algebra over $\F_{7}$

The endomorphism algebra of this simple isogeny class is 6.0.1714608.1.

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
3.7.j_bq_fd	$2$	(not in LMFDB)
3.7.d_a_ah	$3$	(not in LMFDB)
3.7.g_v_ce	$3$	(not in LMFDB)