Properties

Label 2.107.abi_ti
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:  $( 1 - 18 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$
Frobenius angles:  $\pm0.164078095836$, $\pm0.218559897265$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 8280 129366720 1501940639160 17186047922534400 196721124782456201400 2252197315237945134870720 25785344754554266479018444120 295216374187747829868481150156800 3379932271138279167265762589786835480 38696844617893742292389533620173911185600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11298 1226030 131111534 14025944314 1500734167506 160578167903038 17181861759394846 1838459209921183850 196715135693534506818

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.as $\times$ 1.107.aq 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.ac_acw$2$(not in LMFDB)
2.107.c_acw$2$(not in LMFDB)
2.107.bi_ti$2$(not in LMFDB)