Properties

Label 4.5.an_dc_alv_bfi
Base Field $\F_{5}$
Dimension $4$
$p$-rank $4$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$
Frobenius angles:  $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.14758361765$, $\pm0.428216853436$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $4$
Slopes:  $[0, 0, 0, 0, 1, 1, 1, 1]$

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
$A(\F_{q^r})$ 40 280000 254218720 155975680000 99309172184200 62554075118080000 38328173256842243080 23489648805575393280000 14565353388973236279643360 9092594955955713993175000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -7 17 128 637 3253 16382 80353 394077 1954928 9763097

Decomposition

1.5.ae 3 $\times$ 1.5.ab

Base change

This is a primitive isogeny class.