Properties

Label 2.107.abi_te
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:  $1 - 34 x + 498 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.119970636295$, $\pm0.247044539448$
Angle rank:  $2$ (numerical)
Number field:  4.0.304400.3
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8276 129271120 1501439442884 17184671849734400 196718616426332074756 2252194135883532442985680 25785342382311135305655419924 295216374833024842053155651686400 3379932276755216786940972658855285556 38696844628817379541313753907113800738000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11290 1225622 131101038 14025765474 1500732048970 160578153129902 17181861796950558 1838459212976425754 196715135749064739450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.304400.3.
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.bi_te$2$(not in LMFDB)