Properties

Label 3.7.af_z_acp
Base Field $\F_{7}$
Dimension $3$
Ordinary No
$p$-rank $3$

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
Weil polynomial:  $1 - 5 x + 25 x^{2} - 67 x^{3} + 175 x^{4} - 245 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.25355572132$, $\pm0.392015231452$, $\pm0.527736718151$
Angle rank:  $3$ (numerical)
Number field:  6.0.1020415023.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 227 195447 46598333 13750282791 4754564320517 1631767890042423 557759831885507072 191445130551675921543 65712063039813451841747 22538767809948831804524007

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 75 393 2387 16833 117891 822384 5760707 40353423 282468075

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.