Properties

Label 4.5.al_ci_aig_vi
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 71 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.111887224672$, $\pm0.14758361765$, $\pm0.292466693033$, $\pm0.493752400559$
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
$A(\F_{q^r})$ 70 378700 261994390 152413116800 98529792816350 61266667616927500 37498238315499418240 23306761596246922483200 14588230530131581136310070 9112190427730262575095767500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 133 625 3225 16057 78640 391025 1957993 9784125

Decomposition

1.5.ae $\times$ 3.5.ah_bb_act

Base change

This is a primitive isogeny class.