Properties

Label 3.4.ag_p_abc
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 2 x + 3 x^{2} - 8 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.168977707736$, $\pm0.618033150523$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 10 2700 162190 15660000 1129223050 67394810700 4351333716670 282424278960000 17926030748306170 1147516858638067500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 11 35 239 1079 4019 16211 65759 260855 1043651

Decomposition

1.4.ae $\times$ 2.4.ac_d

Base change

This is a primitive isogeny class.