Properties

Label 2.107.abj_ua
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 18 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$
Frobenius angles:  $\pm0.164078095836$, $\pm0.193011390838$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8190 128992500 1501333044120 17185541782500000 196721244968829030450 2252198494309678944120000 25785346971800138708309417730 295216376735636292319789770000000 3379932272717495716714823501282999160 38696844617114470430689289392348012312500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 11265 1225534 131107673 14025952883 1500734953170 160578181710929 17181861907684273 1838459210780173018 196715135689573083825

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.as $\times$ 1.107.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_ado$2$(not in LMFDB)
2.107.b_ado$2$(not in LMFDB)
2.107.bj_ua$2$(not in LMFDB)