Properties

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

Invariants

 Base field: $\F_{7}$ Dimension: $2$ Weil polynomial: $( 1 - 4 x + 7 x^{2} )( 1 - x + 7 x^{2} )$ Frobenius angles: $\pm0.227185525829$, $\pm0.439481140838$ Angle rank: $1$ (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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28 3024 132496 5818176 282879268 13908900096 679257372052 33208310064384 1627398540096784 79782948527388624

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 61 384 2425 16833 118222 824799 5760529 40328448 282442261

Decomposition

1.7.ae $\times$ 1.7.ab

Base change

This is a primitive isogeny class.