Properties

Label 2.107.abh_sf
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:  $1 - 33 x + 473 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0734344692256$, $\pm0.286479328979$
Angle rank:  $2$ (numerical)
Number field:  4.0.16508493.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8359 129455833 1501093229233 17182741714048989 196714489624683441424 2252188573128331854084601 25785337612377586246946406997 295216373338673653712394499875093 3379932279361068138793439957062525819 38696844633594811277819732599430364268288

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11307 1225341 131086315 14025471240 1500728342271 160578123425151 17181861709977955 1838459214393836229 196715135773350779862

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.16508493.1.
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_sf$2$(not in LMFDB)