Properties

Label 4.5.al_cj_aiq_wq
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:  $( 1 - 4 x + 5 x^{2} )( 1 - x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.14758361765$, $\pm0.384619558242$, $\pm0.428216853436$
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
$A(\F_{q^r})$ 70 387100 264466720 138352636800 89100491984350 59623239202508800 37825657596717684190 23415129903752882265600 14543958737660858033842720 9086794725835950470555477500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 136 563 2915 15630 79319 392835 1952056 9756867

Decomposition

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

Base change

This is a primitive isogeny class.