Properties

Label 2.107.abj_tw
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:  $1 - 35 x + 516 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.105531336350$, $\pm0.231854495772$
Angle rank:  $2$ (numerical)
Number field:  4.0.2485400.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8186 128896756 1500817016024 17184058699816736 196718338838794302886 2252194316223902538060736 25785342742415384788376401814 295216374788348492623633946038400 3379932275854373690652234065697319736 38696844627318757300130999154838189834996

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11257 1225114 131096361 14025745683 1500732169138 160578155372449 17181861794350353 1838459212486426798 196715135741446503897

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.2485400.1.
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.bj_tw$2$(not in LMFDB)