Properties

Label 2.7.ad_n
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:  $1 - 3 x + 13 x^{2} - 21 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.285438917538$, $\pm0.518223395765$
Angle rank:  $2$ (numerical)
Number field:  4.0.80613.1
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
$A(\F_{q^r})$ 39 3393 127413 5744349 284731824 13867248681 676148203497 33190716401973 1628776515001779 79808767658949888

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 67 371 2395 16940 117871 821021 5757475 40362599 282533662

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.