Properties

Label 2.113.abi_tf
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 13 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.290579079721$
Angle rank:  $2$ (numerical)
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9393 161042985 2082048021648 26584702995940425 339453931997677361073 4334515395570368456232960 55347514994490787432086748689 706732545433883303422080819225225 9024267967185981305072542180530221712 115230877659143516597630244605140391152425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 80 12612 1442966 163048964 18424199440 2081948051934 235260503533072 26584441656502276 3004041938655930998 339456739027307112132

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.an 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.ai_abv$2$(not in LMFDB)
2.113.i_abv$2$(not in LMFDB)
2.113.bi_tf$2$(not in LMFDB)