Properties

Label 2.7.ac_ad
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:  $1 - 2 x - 3 x^{2} - 14 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0432908094522$, $\pm0.709957476119$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{2}, \sqrt{-3})\)
Galois group:  $V_4$

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 1953 96100 5767209 278449471 13731152400 678843769999 33205288305609 1628065203504100 79799314395126753

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 40 276 2404 16566 116710 824298 5760004 40344972 282500200

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.