Properties

Label 2.107.abi_tf
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:  $( 1 - 19 x + 107 x^{2} )( 1 - 15 x + 107 x^{2} )$
Frobenius angles:  $\pm0.129482033963$, $\pm0.241815531636$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 contains the Jacobians of 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8277 129295017 1501564737456 17185016651539689 196719250667275990077 2252194964065070623984896 25785343080852433730061534309 295216374922951237108434786134025 3379932275820634270367058092356553904 38696844626774200475460261397404101793177

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11292 1225724 131103668 14025810694 1500732600822 160578157480066 17181861802184356 1838459212468074788 196715135738678253132

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.at $\times$ 1.107.ap 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.ae_act$2$(not in LMFDB)
2.107.e_act$2$(not in LMFDB)
2.107.bi_tf$2$(not in LMFDB)