Abelian variety isogeny class 2.17.q_du over $\F_{17}$

• Label: 2.17.q_du
• Base field: $\F_{17}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{17}$
Dimension:	$2$
L-polynomial:	$( 1 + 8 x + 17 x^{2} )^{2}$
	$1 + 16 x + 98 x^{2} + 272 x^{3} + 289 x^{4}$
Frobenius angles:	$\pm0.922020869623$, $\pm0.922020869623$
Angle rank:	$1$ (numerical)
Jacobians:	$0$

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$676$	$67600$	$25180324$	$6922240000$	$2018291883556$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$34$	$230$	$5122$	$82878$	$1421474$	$24135590$	$410327042$	$6975884158$	$118587060514$	$2015998274150$

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 $\F_{17}$.

Endomorphism algebra over $\F_{17}$

The isogeny class factors as 1.17.i^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$

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
2.17.aq_du	$2$	(not in LMFDB)
2.17.a_abe	$2$	(not in LMFDB)
2.17.ai_bv	$3$	(not in LMFDB)