Properties

Label 2.4.ab_a
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1 - x - 4 x^{3} + 16 x^{4}$
Frobenius angles:  $\pm0.180745703069$, $\pm0.702084401492$
Angle rank:  $2$ (numerical)
Number field:  4.0.13068.1
Galois group:  $D_{4}$

This isogeny class is simple.

Newton polygon

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

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
$A(\F_{q^r})$ 12 264 3348 78672 1110972 16867224 275376036 4288725408 68471444556 1099886721384

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 16 52 304 1084 4120 16804 65440 261196 1048936

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.