Properties

Label 5.2.ah_ba_acm_eq_ahc
Base Field $\F_{2}$
Dimension $5$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.615026728081$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 4 5000 114244 6250000 124333484 999635000 18913493876 738112500000 27192179459068 1068490878125000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 8 20 48 76 56 52 160 380 968

Decomposition

1.2.ac 4 $\times$ 1.2.b

Base change

This is a primitive isogeny class.