Properties

Label 3.7.ae_v_abz
Base Field $\F_{7}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
Weil polynomial:  $(1+x+7x^{2})(1-5x+19x^{2}-35x^{3}+49x^{4})$
Frobenius angles:  $\pm0.26035043379$, $\pm0.415892662795$, $\pm0.560518859162$
Angle rank:  $3$ (numerical)

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
$A(\F_{q^r})$ 261 199143 44715564 13712389551 4778766099216 1630429805165616 557488718919809091 191501575080146996175 65708754933069306113292 22536972343702780177552128

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 76 379 2380 16919 117793 821986 5762404 40351393 282445571

Decomposition

1.7.b $\times$ 2.7.af_t

Base change

This is a primitive isogeny class.