Properties

Label 3.13.aq_er_ave
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:  $1 - 16 x + 121 x^{2} - 550 x^{3} + 1573 x^{4} - 2704 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.0339662302293$, $\pm0.236468595294$, $\pm0.337737339224$
Angle rank:  $3$ (numerical)
Number field:  6.0.12178624.2
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

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
$A(\F_{q^r})$ 622 4454764 10900314262 23442910445104 51088586067563662 112297221797497705132 246963725802684757947142 542762482093583037879821056 1192521690621180046710515155582 2619988314736322028316787504697004

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 156 2260 28740 370588 4820016 62722910 815673180 10604396206 137858106216

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.