Properties

Label 2.107.abi_sz
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:  $1 - 34 x + 493 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0719238810965$, $\pm0.266777608024$
Angle rank:  $2$ (numerical)
Number field:  4.0.8129600.2
Galois group:  $D_{4}$
Jacobians:  18

This isogeny class is simple and geometrically 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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8271 129151665 1500813014724 17182940004117225 196715373701996485431 2252189660735823342287760 25785337824480626630920517679 295216371803613695109497146809225 3379932276432633439282449990309049956 38696844631144629551223050141625546926625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11280 1225112 131087828 14025534274 1500729066990 160578124746022 17181861620636068 1838459212800961784 196715135760895298400

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.8129600.2.
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.bi_sz$2$(not in LMFDB)