Properties

Label 1.4.c
Base Field $\F_{2^2}$
Dimension $1$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $1$
Weil polynomial:  $1+2x+4x^{2}$
Frobenius angles:  $\pm0.666666666667$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2]$

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
$A(\F_{q^r})$ 7 21 49 273 1057 3969 16513 65793 261121 1049601

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 21 49 273 1057 3969 16513 65793 261121 1049601

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.