Properties

Label 2.107.abh_sb
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:  $1 - 33 x + 469 x^{2} - 3531 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0184782107058$, $\pm0.296438695563$
Angle rank:  $2$ (numerical)
Number field:  4.0.1890117.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8355 129360465 1500606985365 17181445456939725 196712138388749156400 2252185309823821661433105 25785333806728116307799242785 295216369059949695931460066083125 3379932273922230878647974091324192095 38696844625731243240593577155849535379200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 11299 1224945 131076427 14025303600 1500726167791 160578099725475 17181861460952323 1838459211435469125 196715135733376387414

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1890117.1.
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.bh_sb$2$(not in LMFDB)