Properties

Label 1.27.aj
Base Field $\F_{3^3}$
Dimension $1$
$p$-rank $0$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^3}$
Dimension:  $1$
Weil polynomial:  $1 - 9 x + 27 x^{2}$
Frobenius angles:  $\pm0.166666666667$
Angle rank:  $0$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$

This isogeny class is simple.

Newton polygon

This isogeny class is supersingular.

$p$-rank:  $0$
Slopes:  $[1/2, 1/2]$

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
$A(\F_{q^r})$ 19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 19 703 19684 532171 14355469 387459856 10460530351 282430067923 7625597484988 205891117745743

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.