Properties

Label 2.113.abl_vu
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
Frobenius angles:  $\pm0.110150159186$, $\pm0.205038125192$
Angle rank:  $2$ (numerical)
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9118 160057372 2081419729144 26587186403114944 339462519183652738798 4334530513379495713263616 55347532353172396016025559966 706732557053439966264107101843200 9024267966369572655428891749569593656 115230877646759520939012157403185911949852

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12533 1442528 163064193 18424665517 2081955313298 235260577317997 26584442093583361 3004041938384160944 339456738990825303893

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.au $\times$ 1.113.ar 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 $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ad_aek$2$(not in LMFDB)
2.113.d_aek$2$(not in LMFDB)
2.113.bl_vu$2$(not in LMFDB)