Properties

Label 4.5.am_cs_ake_bax
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:  $( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )^{2}$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.0512862249088$, $\pm0.384619558242$, $\pm0.384619558242$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 49 305809 239754256 132002149041 84618786129409 57482103270113536 37328307093883814449 23386524211874297677329 14551944166392407808553744 9085114642646574814495668049

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 22 126 534 2754 15058 78282 392358 1953126 9755062

Decomposition

2.5.ag_r 2

Base change

This is a primitive isogeny class.