Properties

Label 2.139.abr_bci
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:  $1 - 43 x + 736 x^{2} - 5977 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0124725911818$, $\pm0.191527477370$
Angle rank:  $2$ (numerical)
Number field:  4.0.43928.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14038 366082964 7205854371256 139350121623952928 2692452447301948800538 52020865926592467382152896 1005095180019665113699037088682 19419444455859695708079116940211328 375203088176794147436563335970331350552 7249298871357146940504408755803444011913044

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18945 2683126 373291545 51888849387 7212548981874 1002544337857369 139353666426020913 19370159728473166786 2692452204000905014705

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.43928.1.
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.br_bci$2$(not in LMFDB)