Properties

Label 4.5.al_cf_ahi_si
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0749012311065$, $\pm0.14758361765$, $\pm0.225515375241$, $\pm0.55326212705$
Angle rank:  $4$ (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
$A(\F_{q^r})$ 58 296380 211105384 150921438080 102289949299058 61311750441672640 37227732300849261922 23290811307029403164160 14573500322886707436902248 9094849235129799353382307900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 19 106 619 3345 16066 78073 390755 1956022 9765519

Decomposition

1.5.ae $\times$ 3.5.ah_y_ach

Base change

This is a primitive isogeny class.