Properties

Label 2.113.abm_wo
Base field $\F_{113}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple No
Geometrically simple No
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$
Frobenius angles:  $\pm0.110150159186$, $\pm0.178616545187$
Angle rank:  $2$ (numerical)
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9024 159616512 2080583555904 26586267657928704 339462255327893461824 4334531865816261955862016 55347535993680814193614132032 706732562671514325559667471155200 9024267972125914158703108097235974976 115230877649321093035728983887049946865152

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12498 1441948 163058558 18424651196 2081955962898 235260592792364 26584442304912766 3004041940300359724 339456738998371396818

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.au $\times$ 1.113.as 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.ac_afe$2$(not in LMFDB)
2.113.c_afe$2$(not in LMFDB)
2.113.bm_wo$2$(not in LMFDB)