Properties

Label 2.7.ad_q
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:  $( 1 - 2 x + 7 x^{2} )( 1 - x + 7 x^{2} )$
Frobenius angles:  $\pm0.376624142786$, $\pm0.439481140838$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 42 3780 137592 5594400 274945902 13819740480 680298909486 33259222684800 1628080222787928 79782138419652900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 73 398 2329 16355 117466 826061 5769361 40345346 282439393

Decomposition

1.7.ac $\times$ 1.7.ab

Base change

This is a primitive isogeny class.