Properties

Label 2.8.af_p
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:  $1 - 5 x + 15 x^{2} - 40 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.129861327262$, $\pm0.510838661864$
Angle rank:  $2$ (numerical)
Number field:  4.0.135401.1
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
$A(\F_{q^r})$ 35 4375 252980 16296875 1081190425 69190030000 4402442340695 281478989421875 18018020111977340 1153029447045109375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 70 493 3978 32994 263935 2099248 16777458 134244709 1073842350

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.