Properties

Label 2.7.ad_f
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:  $1 - 3 x + 5 x^{2} - 21 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.130332681249$, $\pm0.613951744591$
Angle rank:  $2$ (numerical)
Number field:  4.0.2725.1
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
$A(\F_{q^r})$ 31 2449 103261 5752701 288791536 13859794681 678773788801 33287020624629 1628811352340059 79789169211245824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 51 299 2395 17180 117807 824213 5774179 40363463 282464286

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.