Properties

Label 2.8.ad_j
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 9 x^{2} - 24 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.203337125451$, $\pm0.587843954393$
Angle rank:  $2$ (numerical)
Number field:  4.0.461353.1
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
$A(\F_{q^r})$ 47 4747 253424 16980019 1097431247 68903958208 4393814682143 281503465731747 18013622985316208 1152786228911734747

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 74 495 4146 33486 262847 2095134 16778914 134211951 1073615834

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.