Properties

Label 3.13.ap_ef_asu
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:  $( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 40 x^{2} - 104 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.22966033005$, $\pm0.383259645523$
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
$A(\F_{q^r})$ 686 4638732 10926245792 23381009108016 51114847857411366 112421676386927432448 247085646745369705463918 542818548136892226822733824 1192527624141034433696590886432 2619985668964138696373481391519212

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 163 2264 28663 370779 4825360 62753879 815757439 10604448968 137857967003

Decomposition

1.13.ah $\times$ 2.13.ai_bo

Base change

This is a primitive isogeny class.