Properties

Label 2.139.abn_yz
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:  $1 - 39 x + 649 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0948109279217$, $\pm0.254073133352$
Angle rank:  $2$ (numerical)
Number field:  4.0.18690957.1
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14511 369029241 7213492497897 139362731528628573 2692465892359233591216 52020874382011314646342329 1005095193167200727225597112093 19419444537351488227861452172185237 375203088493826484272085053655594874803 7249298872196331722708538527256403974080256

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19099 2685971 373325323 51889108496 7212550154191 1002544350971537 139353667010804899 19370159744840214923 2692452204312585489814

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.18690957.1.
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.bn_yz$2$(not in LMFDB)