Abelian variety isogeny class 2.512.adj_eid over $\F_{2^{9}}$

• Label: 2.512.adj_eid
• Base field: $\F_{2^{9}}$
• 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:	$\F_{2^{9}}$
Dimension:	$2$
L-polynomial:	$1 - 87 x + 2915 x^{2} - 44544 x^{3} + 262144 x^{4}$
Frobenius angles:	$\pm0.0534619441191$, $\pm0.114028964195$
Angle rank:	$2$ (numerical)
Number field:	4.0.360225.1
Galois group:	$D_{4}$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$220429$	$68264877439$	$18010195302435556$	$4722333332280037064811$	$1237939851854867103820349659$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$426$	$260406$	$134186409$	$68718994330$	$35184366761736$	$18014398512991287$	$9223372039410585510$	$4722366482970940934194$	$2417851639232173676681433$	$1237940039285451557391143286$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{9}}$.

Endomorphism algebra over $\F_{2^{9}}$

The endomorphism algebra of this simple isogeny class is 4.0.360225.1.

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
2.512.dj_eid	$2$	(not in LMFDB)