Properties

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

Learn more about

Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 39 x + 642 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0204242639044$, $\pm0.272236041847$
Angle rank:  $2$ (numerical)
Number field:  4.0.764725.2
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
$A(\F_{q^r})$ 14504 368749696 7211289070496 139353579590869504 2692439756654449565624 52020817366350744775284736 1005095092760694902881088421464 19419444386498595506744503375202304 375203088277564578166889770643557355936 7249298871840817601119344593035391626907776

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19085 2685152 373300809 51888604811 7212542249126 1002544250819849 139353665928286609 19370159733675520928 2692452204180544474925

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.764725.2.
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_ys$2$(not in LMFDB)