Properties

Label 2.139.abn_yv
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:  $1 - 39 x + 645 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0615603342414$, $\pm0.265172542695$
Angle rank:  $2$ (numerical)
Number field:  4.0.17564677.1
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
$A(\F_{q^r})$ 14507 368869489 7212233373293 139357510790224717 2692451079081707702672 52020842651298249941982289 1005095139881051505247851940361 19419444466319258905823657723912373 375203088416344399862127491143395863831 7249298872112424865603862939587561965270784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19091 2685503 373311339 51888823016 7212545754815 1002544297820621 139353666501078595 19370159740840140299 2692452204281421758486

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.17564677.1.
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.bn_yv$2$(not in LMFDB)