Properties

Label 3.4.ag_w_acb
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 4 x^{2} )( 1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.140237960897$, $\pm0.38771221219$, $\pm0.419569376745$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20 6600 366320 15906000 985810500 69630105600 4580036281820 286602483684000 18010956687551120 1149680054246625000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 25 86 241 939 4150 17051 66721 262094 1045625

Decomposition

1.4.ab $\times$ 2.4.af_n

Base change

This is a primitive isogeny class.