Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $1 - x - x^{2} + 2 x^{3} - 2 x^{4} - 4 x^{5} + 8 x^{6}$
Frobenius angles:  $\pm0.0743927619408$, $\pm0.403891304032$, $\pm0.869099747587$
Angle rank:  $3$ (numerical)
Number field:  6.0.6041764.1
Galois group:  $S_4\times C_2$

This isogeny class is simple.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3 27 684 3051 17193 295488 2074341 21604131 125769132 1091050587

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 2 11 10 12 71 128 322 479 1042

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.