Properties

Label 2.107.abi_tc
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:  $1 - 34 x + 496 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.101476157912$, $\pm0.255918019012$
Angle rank:  $2$ (numerical)
Number field:  4.0.7316288.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8274 129223332 1501188862698 17183980678841424 196717333640553251274 2252192412726496669322628 25785340772891658930881037618 295216374141708108145623151506432 3379932277645275194472155296991453058 38696844631393939737165812851662469165572

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11286 1225418 131095766 14025674014 1500730900758 160578143107246 17181861756715294 1838459213460558554 196715135762162664966

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.7316288.1.
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_tc$2$(not in LMFDB)