Properties

Label 2.107.abi_td
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:  $1 - 34 x + 497 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.110706537265$, $\pm0.251697673458$
Angle rank:  $2$ (numerical)
Number field:  4.0.6193728.2
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8275 129247225 1501314151300 17184326525505625 196717977417428093875 2252193285443346062035600 25785341613067313032308600475 295216374573109289779847788595625 3379932277365647323374650735729812900 38696844630364802866222577399570576853625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11288 1225520 131098404 14025719914 1500731482286 160578148339438 17181861781823236 1838459213308459520 196715135756931054968

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.6193728.2.
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_td$2$(not in LMFDB)