Properties

Label 4.5.al_ci_aih_vm
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 72 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0767028971338$, $\pm0.14758361765$, $\pm0.313688588913$, $\pm0.486729365003$
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
$A(\F_{q^r})$ 68 368560 253973744 145725675520 95113205467828 60413486247562240 37408435140425549492 23303788858944706314240 14584444447485317147745776 9110344141423473374156090800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 25 130 597 3115 15838 78451 390973 1957486 9782145

Decomposition

1.5.ae $\times$ 3.5.ah_bb_acu

Base change

This is a primitive isogeny class.