Properties

Label 2.107.abi_sy
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:  $1 - 34 x + 492 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0604166695618$, $\pm0.269957969854$
Angle rank:  $2$ (numerical)
Number field:  4.0.7101248.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8270 129127780 1500687737990 17182592067592400 196714710853131425350 2252188698732175168306180 25785336698284566441170087630 295216370671288780547419872588800 3379932275322273764399379976901735870 38696844629873053219252588947959445808900

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11278 1225010 131085174 14025487014 1500728425966 160578117732638 17181861554733726 1838459212196999690 196715135754431249118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.7101248.1.
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_sy$2$(not in LMFDB)