Properties

Label 4.5.am_cu_akp_bcc
Base Field $\F_{5}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$
Frobenius angles:  $\pm0.14758361765$, $\pm0.2$, $\pm0.265942140215$, $\pm0.4$
Angle rank:  $2$ (numerical)

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 66 421740 336444768 175781232000 99467228373216 60704070058494720 37575140666632160658 23314520028921029568000 14532517594099089483772896 9086545273779316874774707200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 26 165 714 3259 15911 78800 391154 1950519 9756601

Decomposition

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

Base change

This is a primitive isogeny class.