Properties

Label 2.107.abn_wv
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:  $1 - 39 x + 593 x^{2} - 4173 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0262161664451$, $\pm0.151730065574$
Angle rank:  $2$ (numerical)
Number field:  4.0.6525.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7831 127292905 1497723535489 17180011184046525 196714503393257094256 2252191884069868150608745 25785342082594274303240023429 295216374820626521946979552941525 3379932274098534658002257105703000811 38696844620812052666821423841917908832000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 69 11115 1222587 131065483 14025472224 1500730548495 160578151263417 17181861796228963 1838459211531366699 196715135708369716950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.6525.1.
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.bn_wv$2$(not in LMFDB)