Properties

Label 2.113.abo_yb
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.148111132014$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8835 158632425 2078261714880 26582261508455625 339456624762272208675 4334525200255968255283200 55347529339009214603127816195 706732557219286144429582719455625 9024267968714751212474896122098619840 115230877647920668089776360096237545835625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 12420 1440338 163033988 18424345594 2081952761310 235260564505978 26584442099821828 3004041939164835314 339456738994245908100

Decomposition and endomorphism algebra

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

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_agr$2$(not in LMFDB)
2.113.c_agr$2$(not in LMFDB)
2.113.bo_yb$2$(not in LMFDB)