Properties

Label 2.107.abk_up
Base Field $\F_{107}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 535 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0971505065705$, $\pm0.211972914317$
Angle rank:  $2$ (numerical)
Number field:  4.0.909072.1
Galois group:  $D_{4}$
Jacobians:  14

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8097 128523681 1500202346436 17183498036437161 196718250597527385177 2252194951447240426413072 25785343890130374557862630081 295216375702769177574699681727113 3379932275557036443351934193108703972 38696844625225466572825488851103846106641

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11224 1224612 131092084 14025739392 1500732592414 160578162519840 17181861847570468 1838459212324695036 196715135730805275304

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.909072.1.
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.bk_up$2$(not in LMFDB)