Properties

Label 2.107.abh_sg
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:  $( 1 - 20 x + 107 x^{2} )( 1 - 13 x + 107 x^{2} )$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.283718842690$
Angle rank:  $2$ (numerical)
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8360 129479680 1501214797280 17183064471654400 196715065863966207800 2252189336661777183784960 25785338402618496274362773720 295216374028255948558807418880000 3379932279990000202030150478293583840 38696844634363134316318619765673968358400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11309 1225440 131088777 14025512325 1500728851046 160578128346375 17181861750112273 1838459214735933600 196715135777256544589

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.au $\times$ 1.107.an and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ah_abu$2$(not in LMFDB)
2.107.h_abu$2$(not in LMFDB)
2.107.bh_sg$2$(not in LMFDB)