Abelian variety isogeny class 3.2.c_f_h over $\F_{2}$

• Label: 3.2.c_f_h
• Base field: $\F_{2}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{2}$
Dimension:	$3$
L-polynomial:	$1 + 2 x + 5 x^{2} + 7 x^{3} + 10 x^{4} + 8 x^{5} + 8 x^{6}$
Frobenius angles:	$\pm0.408495174868$, $\pm0.562862561315$, $\pm0.792228845011$
Angle rank:	$3$ (numerical)
Number field:	6.0.400967.1
Galois group:	$A_4\times C_2$
Jacobians:	$1$

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:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$41$	$287$	$533$	$3731$	$20131$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$5$	$11$	$8$	$15$	$20$	$80$	$124$	$263$	$575$	$876$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is not hyperelliptic):

• $x^3 y+x^3 z+x^2 y^2+x z^3+y^3 z=0$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{2}$

The endomorphism algebra of this simple isogeny class is 6.0.400967.1.

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
3.2.ac_f_ah	$2$	3.4.g_r_bj