Properties

Label 2.4.a_e
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 2 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$
Frobenius angles:  $\pm0.333333333333$, $\pm0.666666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 21 441 3969 74529 1049601 15752961 268451841 4328718849 68718952449 1101662259201

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 25 65 289 1025 3841 16385 66049 262145 1050625

Decomposition

1.4.ac $\times$ 1.4.c

Base change

This is a primitive isogeny class.