Properties

Label 2.107.abi_tb
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:  $1 - 34 x + 495 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0920877264428$, $\pm0.259798324418$
Angle rank:  $2$ (numerical)
Number field:  4.0.506432.4
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8273 129199441 1501063577072 17183634309729881 196716685095696810433 2252191517714969522497792 25785339861554865073382737913 295216373537324000305173250056233 3379932277587436213403949711537726704 38696844631882146463689272103882383460241

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11284 1225316 131093124 14025627774 1500730304374 160578137431898 17181861721539588 1838459213429097980 196715135764644460404

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.506432.4.
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_tb$2$(not in LMFDB)