Properties

Label 4.3.ah_ba_acp_fb
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:  $1 - 7 x + 26 x^{2} - 67 x^{3} + 131 x^{4} - 201 x^{5} + 234 x^{6} - 189 x^{7} + 81 x^{8}$
Frobenius angles:  $\pm0.0365491909691$, $\pm0.234353293111$, $\pm0.355928212636$, $\pm0.548250857189$
Angle rank:  $4$ (numerical)
Number field:  8.0.371495353.1
Galois group:  $C_2 \wr S_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 9 8433 556983 38058129 3443813559 266687359281 20994047917929 1808033357296737 150786355400594739 12057431016972414753

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 13 30 73 242 688 1999 6401 19776 58558

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.