Properties

Label 3.5.ai_bg_adh
Base Field $\F_{5}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $3$
Weil polynomial:  $1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.0657033817182$, $\pm0.238557099512$, $\pm0.475140873389$
Angle rank:  $3$ (numerical)
Number field:  6.0.4426955.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25 15275 1980025 231339875 30447855125 3862876313075 476458348531225 59283223224723875 7437174098712049600 931818740873960853875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 26 127 594 3118 15821 78062 388514 1949608 9770826

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.