Properties

Label 2.139.abp_bao
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:  $1 - 41 x + 690 x^{2} - 5699 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0422463462183$, $\pm0.231214793371$
Angle rank:  $2$ (numerical)
Number field:  4.0.650133.2
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
$A(\F_{q^r})$ 14272 367532544 7209466033408 139355252115843072 2692454435843796503872 52020855377506881551130624 1005095149572786362316171021376 19419444421981954289699814558179328 375203088219346280154042143110400640256 7249298871662079036448625707850426948381184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19021 2684472 373305289 51888887709 7212547519270 1002544307487759 139353666182914705 19370159730669954696 2692452204114159428461

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.650133.2.
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_bao$2$(not in LMFDB)