Properties

Label 2.107.abn_ww
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:  $( 1 - 20 x + 107 x^{2} )( 1 - 19 x + 107 x^{2} )$
Frobenius angles:  $\pm0.0823304377774$, $\pm0.129482033963$
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
$A(\F_{q^r})$ 7832 127316992 1497867399776 17180497637822464 196715709548079020552 2252194329555486174724096 25785346363271793039272617064 295216381485538107227006493081600 3379932283484423550166948459493915744 38696844632866934567326724037485030167552

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 69 11117 1222704 131069193 14025558219 1500732178022 160578177921321 17181862184132881 1838459216636668368 196715135769650623757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.au $\times$ 1.107.at 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_agk$2$(not in LMFDB)
2.107.b_agk$2$(not in LMFDB)
2.107.bn_ww$2$(not in LMFDB)