Properties

Label 2.7.ak_bn
Base Field $\F_{7}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 7 x^{2} )^{2}$
Frobenius angles:  $\pm0.106147807505$, $\pm0.106147807505$
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
$A(\F_{q^r})$ 9 1521 104976 5659641 283349889 13908900096 680293390401 33282226355625 1629429133651344 79810905102881121

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 28 304 2356 16858 118222 826054 5773348 40378768 282541228

Decomposition

1.7.af 2

Base change

This is a primitive isogeny class.