Properties

Label 2.139.abp_bar
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:  $1 - 41 x + 693 x^{2} - 5699 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0825424652016$, $\pm0.219145610075$
Angle rank:  $2$ (numerical)
Number field:  4.0.3618405.2
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
$A(\F_{q^r})$ 14275 367652625 7210459053925 139359685241338125 2692468381320814102000 52020889741972184465048625 1005095219259897076334873455825 19419444541268004303014626226563125 375203088395004546830899044606962326975 7249298871893020036145559074584437640800000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19027 2684841 373317163 51889156464 7212552283807 1002544376998011 139353667038909763 19370159739738453309 2692452204199932910102

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.3618405.2.
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.bp_bar$2$(not in LMFDB)