Properties

Label 2.107.abh_sh
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 33 x + 475 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0906927404122$, $\pm0.280822468292$
Angle rank:  $2$ (numerical)
Number field:  4.0.215725.1
Galois group:  $D_{4}$
Jacobians:  55

This isogeny class is simple and geometrically 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 55 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8361 129503529 1501336368171 17183386706613741 196715637475387793136 2252190079314176884106481 25785339128835949274511401631 295216374568611505863153204181269 3379932280338716852568793832862549429 38696844634692158064963532970767849415424

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11311 1225539 131091235 14025553080 1500729345907 160578132868893 17181861781561459 1838459214925612353 196715135778929134486

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.215725.1.
All geometric endomorphisms are defined over $\F_{107}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.bh_sh$2$(not in LMFDB)