Properties

Label 2.107.abo_xq
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:  $( 1 - 20 x + 107 x^{2} )^{2}$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.0823304377774$
Angle rank:  $1$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 7744 126877696 1496864159296 17178795458953216 196713315249072998464 2252191449954175912247296 25785343434737831981758866496 295216379162865095316382679040000 3379932282580397596266764811466283584 38696844634240784758505023714179857514496

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 68 11078 1221884 131056206 14025387508 1500730259222 160578159683884 17181862048951198 1838459216144938148 196715135776634581478

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.au 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$
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_ahe$2$(not in LMFDB)
2.107.bo_xq$2$(not in LMFDB)
2.107.u_lh$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.a_ahe$2$(not in LMFDB)
2.107.bo_xq$2$(not in LMFDB)
2.107.u_lh$3$(not in LMFDB)
2.107.a_he$4$(not in LMFDB)
2.107.au_lh$6$(not in LMFDB)