Properties

Label 3.4.ai_bg_adb
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:  $( 1 - 3 x + 4 x^{2} )( 1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4} )$
Frobenius angles:  $\pm0.140237960897$, $\pm0.230053456163$, $\pm0.38771221219$
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
$A(\F_{q^r})$ 10 4400 356680 19087200 1106480250 70308761600 4486981926010 283673699179200 17995934004404680 1150198391157750000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 17 84 289 1057 4190 16713 66049 261876 1046097

Decomposition

1.4.ad $\times$ 2.4.af_n

Base change

This is a primitive isogeny class.