Properties

Label 2.7.aj_bi
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:  $( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.227185525829$
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
$A(\F_{q^r})$ 12 1872 117936 5937984 286901652 13908900096 678839269764 33234302649600 1628413520361264 79795347091651152

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 37 344 2473 17069 118222 824291 5765041 40353608 282486157

Decomposition

1.7.af $\times$ 1.7.ae

Base change

This is a primitive isogeny class.