Properties

Label 3.3.ae_j_ar
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 36 x^{5} + 27 x^{6}$
Frobenius angles:  $\pm0.065336691368$, $\pm0.328985474983$, $\pm0.609104440316$
Angle rank:  $3$ (numerical)
Number field:  6.0.10338167.1
Galois group:  $S_4\times C_2$

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
$A(\F_{q^r})$ 7 847 14308 502271 14422352 339328528 9863032277 292370442287 7771038924292 206089871896832

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 12 21 76 245 633 2058 6788 20055 59107

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.