Properties

Label 2.169.abs_bfc
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:  $1 - 44 x + 808 x^{2} - 7436 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.0449093466818$, $\pm0.252181585824$
Angle rank:  $2$ (numerical)
Number field:  4.0.14362880.1
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21890 806646500 23294046862130 665423815855370000 19004955701325285042450 542800612104003946591398500 15502932164795167161755753892770 442779262228407092408733446481920000 12646218550443873311595380911734303283010 361188648084055844278856303330219084420662500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 28242 4825974 815739558 137858433286 23298078329202 3937376223696174 665416606856166078 112455406931625121566 19004963774855774310802

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.14362880.1.
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_bfc$2$(not in LMFDB)