Properties

Label 2.27.an_di
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 86 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.116708562514$, $\pm0.397192792614$
Angle rank:  $2$ (numerical)
Number field:  4.0.566497.1
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
$A(\F_{q^r})$ 452 533360 389477552 282136772800 205810748983852 150098136476130560 109422434893079867836 79766991465875097465600 58149768794530247203283888 42391157502680052854208258800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 733 19788 530889 14343305 387429526 10460682611 282431478161 7625601654036 205891128342493

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.