Properties

Label 2.113.abj_uk
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:  $( 1 - 19 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$
Frobenius angles:  $\pm0.148111132014$, $\pm0.228810695365$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9310 160969900 2083267120480 26589651961600000 339464667533711745550 4334531080902907276537600 55347530368934151536407770670 706732552458568825561930521600000 9024267960151216182412493894174393440 115230877640250356714979121954014471947500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12605 1443808 163079313 18424782119 2081955585890 235260568883783 26584441920742753 3004041936314164384 339456738971650064525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.at $\times$ 1.113.aq 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ad_ada$2$(not in LMFDB)
2.113.d_ada$2$(not in LMFDB)
2.113.bj_uk$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ad_ada$2$(not in LMFDB)
2.113.d_ada$2$(not in LMFDB)
2.113.bj_uk$2$(not in LMFDB)
2.113.abh_sy$4$(not in LMFDB)
2.113.af_abo$4$(not in LMFDB)
2.113.f_abo$4$(not in LMFDB)
2.113.bh_sy$4$(not in LMFDB)