Properties

Label 4.3.am_co_aii_rr
Base Field $\F_{3}$
Dimension $4$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )^{4}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 2401 614656 68574961 5393580481 377801998336 26505620986321 1947408269043601 150125140011540736 11959584699384036001

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -8 -2 28 118 352 946 2512 6886 19684 58078

Decomposition

1.3.ad 4

Base change

This is a primitive isogeny class.