Properties

Label 3.2.ac_a_d
Base Field $\F_{2}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.0889496890695$, $\pm0.297004294965$, $\pm0.823081333977$
Angle rank:  $3$ (numerical)
Number field:  6.0.1539727.2
Galois group:  $D_{6}$

This isogeny class is simple.

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 6 7 8 9 10
$A(\F_{q^r})$ 2 32 632 6976 23342 283136 1655194 17984128 155066888 1154401952

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 1 10 25 21 70 99 273 586 1101

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.