Properties

Label 2.27.an_de
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:  $1 - 13 x + 82 x^{2} - 351 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0478883640571$, $\pm0.415544989003$
Angle rank:  $2$ (numerical)
Number field:  4.0.198189.1
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
$A(\F_{q^r})$ 448 526848 386385664 281414805504 205706344475968 150084865347379200 109419982771982327872 79766492662531177488384 58149699123636351300810496 42391152665604676745954032128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 15 725 19632 529529 14336025 387395270 10460448195 282429712049 7625592517584 205891104849125

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.