Properties

Label 4.5.al_ce_aha_ri
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:  $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6} )$
Frobenius angles:  $\pm0.0441569735346$, $\pm0.14758361765$, $\pm0.210407616474$, $\pm0.568817170463$
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
$A(\F_{q^r})$ 54 270540 195495606 148498323840 101585855236734 60772837352036940 37124083642174038144 23284050299033598973440 14555721144181616923404438 9085575765610606761485642700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 17 97 609 3325 15929 77856 390641 1953637 9755557

Decomposition

1.5.ae $\times$ 3.5.ah_x_acd

Base change

This is a primitive isogeny class.