Properties

Label 2.107.abm_wb
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:  $1 - 38 x + 573 x^{2} - 4066 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0518582790060$, $\pm0.176577017397$
Angle rank:  $2$ (numerical)
Number field:  4.0.85568.1
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
$A(\F_{q^r})$ 7919 127709713 1498591021508 17181287417996969 196715955961391631799 2252193146172366371840656 25785342805204137703968084527 295216374887219624331196870813193 3379932273833528863380292957536813284 38696844621093445241535630900612324587713

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 70 11152 1223296 131075220 14025575790 1500731389486 160578155763466 17181861800104740 1838459211387221104 196715135709800174112

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.85568.1.
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.bm_wb$2$(not in LMFDB)