Properties

Label 2.107.abk_us
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:  $( 1 - 18 x + 107 x^{2} )^{2}$
Frobenius angles:  $\pm0.164078095836$, $\pm0.164078095836$
Angle rank:  $1$ (numerical)
Jacobians:  36

This isogeny class is not 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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8100 128595600 1500600500100 17184692972160000 196720749987234502500 2252198934054403712960400 25785348771021852620760524100 295216379858606794227674818560000 3379932276461665888148165602485080100 38696844620138351364900982193687560890000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 11230 1224936 131101198 14025917592 1500735246190 160578192915576 17181862089443998 1838459212816753512 196715135704944961150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-26}) \)$)$
All geometric endomorphisms are defined over $\F_{107}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.a_aeg$2$(not in LMFDB)
2.107.bk_us$2$(not in LMFDB)
2.107.s_ij$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.a_aeg$2$(not in LMFDB)
2.107.bk_us$2$(not in LMFDB)
2.107.s_ij$3$(not in LMFDB)
2.107.a_eg$4$(not in LMFDB)
2.107.as_ij$6$(not in LMFDB)