Properties

Label 4.5.am_ct_akk_bbo
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.14758361765$, $\pm0.35241638235$, $\pm0.384619558242$
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
$A(\F_{q^r})$ 56 353920 279579104 148816281600 89660131438136 58528118482462720 37529051753962714232 23460952075775882035200 14580523303619111741790944 9090031340992850449276969600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 24 144 608 2934 15342 78702 393600 1956960 9760344

Decomposition

1.5.ae $\times$ 1.5.ac $\times$ 2.5.ag_r

Base change

This is a primitive isogeny class.