Properties

Label 2.27.as_ff
Base Field $\F_{3^3}$
Dimension $2$
$p$-rank $0$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 27 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 361 494209 387459856 283205973241 206079490209961 150125140011540736 109422695224192183201 79766743266990393533929 58149737003055310885360144 42391152366591408085994622049

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 676 19684 532900 14362030 387499222 10460707498 282430599364 7625597484988 205891103396836

Decomposition

1.27.aj 2

Base change

This is a primitive isogeny class.