Properties

Label 2.7.ae_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:  $1 - 4 x + 16 x^{2} - 28 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.27676332829$, $\pm0.464689692576$
Angle rank:  $2$ (numerical)
Number field:  4.0.28928.2
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
$A(\F_{q^r})$ 34 3332 133858 5771024 281756674 13865814788 677804095618 33193822011392 1627968017262178 79803570767082372

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 66 388 2406 16764 117858 823036 5758014 40342564 282515266

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.