Properties

Label 3.13.aq_et_avp
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:  $( 1 - 5 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.129998747777$, $\pm0.256122854178$, $\pm0.292104599859$
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
$A(\F_{q^r})$ 639 4601439 11225100852 23833986160959 51390434008460304 112449530624823290304 247013033277756500911683 542782277828473768235592975 1192549044869162504826166878804 2620020318392502099884099810974464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 160 2323 29212 372773 4826557 62735440 815702932 10604639449 137859790175

Decomposition

1.13.af $\times$ 2.13.al_cd

Base change

This is a primitive isogeny class.