Properties

Label 3.4.ag_q_abg
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.2$, $\pm0.6$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 11 3069 178409 15728625 1139670081 67645734849 4296032714369 280375465082625 17909119735298561 1146182576381093889

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 13 41 241 1089 4033 16001 65281 260609 1042433

Decomposition

1.4.ae $\times$ 2.4.ac_e

Base change

This is a primitive isogeny class.