Properties

Label 3.13.ap_ef_asv
Base Field $\F_{13}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $1 - 15 x + 109 x^{2} - 489 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$
Frobenius angles:  $\pm0.0482491347716$, $\pm0.243527616942$, $\pm0.379270569548$
Angle rank:  $3$ (numerical)
Number field:  6.0.296888383.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 685 4632655 10907274865 23331278233575 51035015651132425 112338752869076393455 247025864572125233807680 542787728252166194461755975 1192515679248513143466178585885 2619980793491707865286568425897775

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 163 2261 28603 370199 4821799 62738696 815711123 10604342747 137857710463

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 6.0.296888383.1.
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.p_ef_sv$2$(not in LMFDB)