Properties

Label 2.169.abu_bhh
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:  $1 - 46 x + 865 x^{2} - 7774 x^{3} + 28561 x^{4}$
Frobenius angles:  $\pm0.111746331041$, $\pm0.188213296655$
Angle rank:  $2$ (numerical)
Number field:  4.0.1074752.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 21607 804795929 23291875918108 665442128117176697 19005083179182936672247 542801091768469716609536144 15502933453632211077872761155991 442779264783309257588207924438049833 12646218553750233938815970449552658083036 361188648084533847114587593371427358758526409

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 28176 4825522 815762004 137859357984 23298098917350 3937376551030144 665416610695718820 112455406961026648066 19004963774880925783936

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13^{2}}$
The endomorphism algebra of this simple isogeny class is 4.0.1074752.1.
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.bu_bhh$2$(not in LMFDB)