Properties

Label 1.107.as
Base Field $\F_{107}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{107}$
Dimension:  $1$
L-polynomial:  $1 - 18 x + 107 x^{2}$
Frobenius angles:  $\pm0.164078095836$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-26}) \)
Galois group:  $C_2$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 90 11340 1224990 131090400 14025717450 1500732799020 160578170281710 17181861943881600 1838459212618454010 196715135716950746700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 90 11340 1224990 131090400 14025717450 1500732799020 160578170281710 17181861943881600 1838459212618454010 196715135716950746700

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-26}) \).
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
1.107.s$2$(not in LMFDB)