Properties

Label 2.139.abn_yy
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:  $1 - 39 x + 648 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0871410937773$, $\pm0.257078959530$
Angle rank:  $2$ (numerical)
Number field:  4.0.793432.1
Galois group:  $D_{4}$
Jacobians:  42

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 42 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14510 368989300 7213177710920 139361428579060000 2692462219392528300050 52020866661489458633099200 1005095180862986140145694376130 19419444523337706445981646817360000 375203088485658750823447232862170468840 7249298872203517016496532606915292170832500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19097 2685854 373321833 51889037711 7212549083762 1002544338698549 139353666910242193 19370159744418549146 2692452204315254169977

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.793432.1.
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_yy$2$(not in LMFDB)