Properties

Label 2.107.abh_se
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:  $1 - 33 x + 472 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0637283762988$, $\pm0.289119628508$
Angle rank:  $2$ (numerical)
Number field:  4.0.14633496.1
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8358 129431988 1500971664024 17182418433786144 196713908757529881018 2252187788695827219518400 25785336757890656182881647562 295216372498458869707285983348864 3379932278445882747245517461658696696 38696844632367404466320071590050908491828

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11305 1225242 131083849 14025429825 1500727819570 160578118103835 17181861661076689 1838459213896036014 196715135767111266025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.14633496.1.
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_se$2$(not in LMFDB)