Properties

Label 2.139.abs_bdg
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:  $1 - 44 x + 760 x^{2} - 6116 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0377284713884$, $\pm0.162150612510$
Angle rank:  $2$ (numerical)
Number field:  4.0.65792.3
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13922 365341124 7203929001458 139347325722259472 2692452179043897658722 52020878287578306518684804 1005095225667040478641932767666 19419444566565759988453548060459008 375203088386388421573704760984301769506 7249298871675802259966688807960908984924484

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 96 18906 2682408 373284054 51888844216 7212550695690 1002544383388896 139353667220446110 19370159739293638944 2692452204119256352186

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.65792.3.
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.bs_bdg$2$(not in LMFDB)