Properties

Label 4.2.af_m_au_bd
Base Field $\F_{2}$
Dimension $4$
Ordinary No
$p$-rank $4$
Contains a Jacobian No

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Invariants

Base field:  $\F_{2}$
Dimension:  $4$
Weil polynomial:  $1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8}$
Frobenius angles:  $\pm0.0635622003031$, $\pm0.165221137389$, $\pm0.365221137389$, $\pm0.663562200303$
Angle rank:  $2$ (numerical)
Number field:  8.0.13140625.1
Galois group:  $C_2^2:C_4$

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
$A(\F_{q^r})$ 1 211 1861 88831 1046771 12172801 344358281 5598573775 68193052891 1095729526441

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 4 4 20 33 46 159 324 508 1019

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.