Properties

Label 4.5.al_ch_ahz_um
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0605820805461$, $\pm0.14758361765$, $\pm0.287119770935$, $\pm0.511693182811$
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
$A(\F_{q^r})$ 64 340480 236305216 145954242560 97099396455424 60419585726456320 37120951071118044992 23226689054721740636160 14577807273559580351296576 9108081009512793909929574400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 23 121 599 3180 15839 77849 389679 1956595 9779718

Decomposition

1.5.ae $\times$ 3.5.ah_ba_acq

Base change

This is a primitive isogeny class.