Properties

Label 2.169.abs_bff
Base Field $\F_{13^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13^{2}}$
Dimension:  $2$
L-polynomial:  $1 - 44 x + 811 x^{2} - 7436 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0731415089542$, $\pm0.244787210186$
Angle rank:  $2$ (numerical)
Number field:  4.0.22196240.1
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21893 806822729 23295960974804 665434843684425785 19004999920929452618973 542800749495696592374649616 15502932514128958005913840551773 442779262987437940556238699180513065 12646218551952126660256965275875774357844 361188648087159859268823118553707426272315129

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28248 4826370 815753076 137858754046 23298084226326 3937376312418654 665416607996851236 112455406945037134290 19004963775019100851528

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.22196240.1.
All geometric endomorphisms are defined over $\F_{13^{2}}$.

Base change

This is a primitive isogeny class.

Twists

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