Properties

Label 2.139.abp_bau
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:  $( 1 - 22 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$
Frobenius angles:  $\pm0.117174211439$, $\pm0.201746658314$
Angle rank:  $2$ (numerical)
Jacobians:  12

This isogeny class is not 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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14278 367772724 7211452111864 139364104961648160 2692482135346412639098 52020922682124690210012096 1005095281582266730038402829258 19419444630918487938498711760448640 375203088472309216431017324620185208024 7249298871845690387189460158870626553418804

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 19033 2685210 373329001 51889421529 7212556850866 1002544439162211 139353667682240401 19370159743729368750 2692452204182354269753

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.aw $\times$ 1.139.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_afk$2$(not in LMFDB)
2.139.d_afk$2$(not in LMFDB)
2.139.bp_bau$2$(not in LMFDB)