Properties

Label 2.7.af_q
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:  $1 - 5 x + 16 x^{2} - 35 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.169178782589$, $\pm0.473594973839$
Angle rank:  $2$ (numerical)
Number field:  4.0.57800.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 26 2756 121784 5666336 284585886 13993468736 680297445854 33223427868800 1628029116513176 79793296617432996

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 57 354 2361 16933 118938 826059 5763153 40344078 282478897

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.