Properties

Label 4.5.al_cg_ahr_tm
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0320471084245$, $\pm0.14758361765$, $\pm0.265942140215$, $\pm0.532047108424$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 60 313200 219424320 145324800000 98138950212300 60215703332428800 36901417148640103980 23174240800525516800000 14559332356987392903013440 9098186160655460922487830000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 21 112 597 3215 15786 77387 388797 1954120 9769101

Decomposition

1.5.ae $\times$ 1.5.ad $\times$ 2.5.ae_i

Base change

This is a primitive isogeny class.