Properties

Label 3.2.ac_c_ab
Base Field $\F_{2}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
L-polynomial:  $1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.161334789180$, $\pm0.327009058845$, $\pm0.739882802642$
Angle rank:  $3$ (numerical)
Number field:  6.0.2464727.1
Galois group:  $S_4\times C_2$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 104 592 11024 31604 246272 2553436 16778528 154949488 1118339144

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 5 10 33 31 62 155 257 586 1065

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2}$
The endomorphism algebra of this simple isogeny class is 6.0.2464727.1.
All geometric endomorphisms are defined over $\F_{2}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.2.c_c_b$2$3.4.a_i_ab