Properties

Label 3.2.ac_g_ah
Base Field $\F_{2}$
Dimension $3$
Ordinary No
$p$-rank $3$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.306143893905$, $\pm0.384973271919$, $\pm0.570118980449$
Angle rank:  $3$ (numerical)

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
$A(\F_{q^r})$ 10 440 1120 4400 30250 197120 1640810 19087200 156684640 1039511000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 13 16 17 31 46 99 289 592 993

Decomposition

1.2.ab $\times$ 2.2.ab_d

Base change

This is a primitive isogeny class.