Properties

Label 4.5.al_cj_aio_wi
Base Field $\F_{5}$
Dimension $4$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
Weil polynomial:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 28 x^{2} - 75 x^{3} + 140 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.117658111351$, $\pm0.14758361765$, $\pm0.327130732663$, $\pm0.462990021908$
Angle rank:  $4$ (numerical)

Newton polygon

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

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
$A(\F_{q^r})$ 74 407740 280608296 151261754240 95397532510834 60862715950229440 37778120833792126274 23401661133629045399040 14585586808425220946415848 9106486304538120500625312700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 27 142 619 3125 15954 79221 392611 1957642 9778007

Decomposition

1.5.ae $\times$ 3.5.ah_bc_acx

Base change

This is a primitive isogeny class.