Properties

Label 2.7.ac_ac
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:  $1 - 2 x - 2 x^{2} - 14 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0805195460407$, $\pm0.700955651792$
Angle rank:  $2$ (numerical)
Number field:  4.0.2312.1
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
$A(\F_{q^r})$ 32 2048 97952 5832704 281130912 13772834816 679953141536 33235867271168 1628456152087328 79809530414450688

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 42 282 2430 16726 117066 825642 5765310 40354662 282536362

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.