Properties

Label 2.107.abj_tr
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:  $1 - 35 x + 511 x^{2} - 3745 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0379397215901$, $\pm0.253680484348$
Angle rank:  $2$ (numerical)
Number field:  4.0.1813925.2
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8181 128777121 1500172050519 17182193095441341 196714595743711577136 2252188558018586046200121 25785335667607647066812295459 295216367764238022214970868143925 3379932270210732508533802840442019081 38696844623457354092384920438886859338496

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11247 1224589 131082131 14025478808 1500728332203 160578111314099 17181861385540723 1838459209416659923 196715135721817088022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.1813925.2.
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.bj_tr$2$(not in LMFDB)