Properties

Label 2.7.ad_o
Base Field $\F_{7}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 7 x^{2} )( 1 + 7 x^{2} )$
Frobenius angles:  $\pm0.308124534521$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 40 3520 130720 5702400 281954200 13850045440 676907873080 33202224000000 1628801557497760 79810950586417600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 69 380 2377 16775 117726 821945 5759473 40363220 282541389

Decomposition

1.7.ad $\times$ 1.7.a

Base change

This is a primitive isogeny class.