Properties

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

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Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )^{2}$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.0540867239847$, $\pm0.445913276015$, $\pm0.445913276015$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 4 4624 391876 21381376 2428715524 283130410000 23991364017604 1816019815366656 145706642016575236 12158462041948282384

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 20 26 156 730 2292 6426 19100 59050

Decomposition

2.3.ae_i 2

Base change

This is a primitive isogeny class.