Properties

Label 2.17.aj_bt
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 45 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.13256323974$, $\pm0.443398416497$
Angle rank:  $2$ (numerical)
Number field:  4.0.1003477.1
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
$A(\F_{q^r})$ 173 85981 24276917 6943911541 2015023398608 582926673437437 168409777454100173 48662164034104184613 14063069918615304820709 4064233209360549492822016

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 299 4941 83139 1419174 24150179 410416533 6975896803 118587753945 2015994794654

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.