Properties

Label 2.139.abq_bbp
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 42 x + 717 x^{2} - 5838 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.100495437984$, $\pm0.187984873465$
Angle rank:  $2$ (numerical)
Number field:  4.0.591424.1
Galois group:  $D_{4}$
Jacobians:  7

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 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14159 366987121 7209169651172 139359557580163561 2692475608143040452599 52020917006679839138506384 1005095283250287402703188970799 19419444649003305800128254302586249 375203088513243417469677524119687781252 7249298871904599518782892076773875344732001

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18992 2684360 373316820 51889295738 7212556063982 1002544440825998 139353667812016804 19370159745842629640 2692452204204233629952

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.591424.1.
All geometric endomorphisms are defined over $\F_{139}$.

Base change

This is a primitive isogeny class.

Twists

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