Properties

Label 3.4.ah_v_abs
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:  $( 1 - 2 x )^{2}( 1 - 3 x + 5 x^{2} - 12 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.103279877171$, $\pm0.563386789496$
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
$A(\F_{q^r})$ 7 2331 153664 13111875 1065967147 68158589184 4306461499963 281202529111875 18081262212629056 1151989153308438291

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 10 31 194 1018 4063 16042 65474 263119 1047730

Decomposition

1.4.ae $\times$ 2.4.ad_f

Base change

This is a primitive isogeny class.