Properties

Label 2.139.abp_bap
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:  $1 - 41 x + 691 x^{2} - 5699 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0577546537355$, $\pm0.227538408547$
Angle rank:  $2$ (numerical)
Number field:  4.0.145493.1
Galois group:  $D_{4}$
Jacobians:  15

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 15 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14273 367572569 7209797036099 139356731313834125 2692459105608550905648 52020866990729905911716801 1005095173623005147759842667783 19419444465066572045703872621367125 375203088289039663337171888124038537789 7249298871771152861652872512592279349775104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19023 2684595 373309251 51888977704 7212549129411 1002544331476941 139353666492089331 19370159734267931385 2692452204154670389078

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.145493.1.
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.bp_bap$2$(not in LMFDB)