Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $3$
Weil polynomial:  $1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.10143524516$, $\pm0.306436956418$, $\pm0.413672014132$
Angle rank:  $3$ (numerical)
Number field:  6.0.1178891.1
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

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
$A(\F_{q^r})$ 29 18299 2375477 244639331 29396710169 3778792413227 479093711198173 59842076388306563 7461702113779025216 931959983641771080779

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 30 151 626 3008 15477 78496 392178 1956040 9772310

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.