Properties

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

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 113 x^{2} )^{2}$
Frobenius angles:  $\pm0.110150159186$, $\pm0.110150159186$
Angle rank:  $1$ (numerical)
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8836 158659216 2078435455684 26582897240805376 339458327210053271236 4334528918811578125200016 55347536324836887753497270404 706732568824316317347730268160000 9024267985987220330078728605189810436 115230877670989670770259870006704555966096

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 12422 1440458 163037886 18424437994 2081954547398 235260594199978 26584442536356478 3004041944914578314 339456739062204502022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.au 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-13}) \)$)$
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_ags$2$(not in LMFDB)
2.113.bo_yc$2$(not in LMFDB)
2.113.u_lb$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_ags$2$(not in LMFDB)
2.113.bo_yc$2$(not in LMFDB)
2.113.u_lb$3$(not in LMFDB)
2.113.a_gs$4$(not in LMFDB)
2.113.au_lb$6$(not in LMFDB)