Properties

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

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 4 x^{2} )( 1 - 3 x + 4 x^{2} )^{2}$
Frobenius angles:  $\pm0.230053456163$, $\pm0.230053456163$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 12 5376 443556 22643712 1162528932 68158589184 4318262438628 278728606420992 17947397694538404 1151408608047134976

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 19 99 335 1107 4063 16083 64895 261171 1047199

Decomposition

1.4.ad 2 $\times$ 1.4.ac

Base change

This is a primitive isogeny class.