Properties

Label 4.2.ae_f_c_al
Base Field $\F_{2}$
Dimension $4$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $4$
Weil polynomial:  $1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8}$
Frobenius angles:  $\pm0.0247483856139$, $\pm0.177336015878$, $\pm0.344002682545$, $\pm0.858081718947$
Angle rank:  $2$ (numerical)
Number field:  8.0.22581504.2
Galois group:  $D_4\times C_2$

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 61 5044 76921 660661 15999568 207872197 4902098409 64314697252 1032534524341

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 -1 11 19 19 65 97 291 479 959

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.