Properties

Label 2.27.aq_ej
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:  $1 - 16 x + 113 x^{2} - 432 x^{3} + 729 x^{4}$
Frobenius angles:  $\pm0.0552645386854$, $\pm0.312858045398$
Angle rank:  $2$ (numerical)
Number field:  4.0.6025.1
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
$A(\F_{q^r})$ 395 509945 388022720 282379494025 205799105639875 150072809526087680 109416474830297860795 79766391490550973902025 58149771909258090724560320 42391164681076649164393423625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 700 19716 531348 14342492 387364150 10460112836 282429353828 7625602062492 205891163207500

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.