Properties

Label 2.7.ah_ba
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:  $( 1 - 4 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )$
Frobenius angles:  $\pm0.227185525829$, $\pm0.308124534521$
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
$A(\F_{q^r})$ 20 2640 138320 6177600 285913100 13803229440 676490325020 33206650963200 1628293788190160 79795216033381200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 53 400 2569 17011 117326 821437 5760241 40350640 282485693

Decomposition

1.7.ae $\times$ 1.7.ad

Base change

This is a primitive isogeny class.