Properties

Label 2.4.ab_d
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 - x + 3 x^{2} - 4 x^{3} + 16 x^{4}$
Frobenius angles:  $\pm0.254152667512$, $\pm0.647800160692$
Angle rank:  $2$ (numerical)
Number field:  4.0.46305.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 15 375 3780 76875 1143825 16254000 265693695 4289701875 68323148460 1099644759375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 22 61 298 1114 3967 16216 65458 260629 1048702

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.