Properties

Label 3.13.ap_dz_are
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 34 x^{2} - 104 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.104164352389$, $\pm0.448054596667$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 644 4273584 10238497472 22856905042944 51016152313775124 112539965532274732032 247170331084403268714116 542837458761077365592211456 1192546278982659896218419027392 2620019421645100182730662587955504

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 151 2120 28015 370059 4830436 62775383 815785855 10604614856 137859742991

Decomposition

1.13.ah $\times$ 2.13.ai_bi

Base change

This is a primitive isogeny class.