Properties

Label 2.2.c_f
Base Field $\F_{2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $( 1 + x + 2 x^{2} )^{2}$
Frobenius angles:  $\pm0.615026728081$, $\pm0.615026728081$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 16 64 16 256 1936 3136 13456 82944 258064 937024

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 11 -1 15 55 47 103 319 503 911

Decomposition

1.2.b 2

Base change

This is a primitive isogeny class.