Properties

Label 2.7.ad_e
Base Field $\F_{7}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 7 x^{2} )( 1 + 2 x + 7 x^{2} )$
Frobenius angles:  $\pm0.106147807505$, $\pm0.623375857214$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30 2340 100440 5709600 287002650 13819740480 678636369210 33285255120000 1628747025806520 79794536858021700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 49 290 2377 17075 117466 824045 5773873 40361870 282483289

Decomposition

1.7.af $\times$ 1.7.c

Base change

This is a primitive isogeny class.