Properties

Label 2.107.abi_sx
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:  $1 - 34 x + 491 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:  $\pm0.0468897983382$, $\pm0.272970800803$
Angle rank:  $2$ (numerical)
Number field:  4.0.325008.5
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8269 129103897 1500562464208 17182243608572809 196714043236242414949 2252187714361790958308608 25785335500010135284772993773 295216369359983505364513181669577 3379932273847655473690464439763620048 38696844627968841262477236742861219518697

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11276 1224908 131082516 14025439414 1500727770038 160578110270386 17181861478414564 1838459211394905044 196715135744751201116

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The endomorphism algebra of this simple isogeny class is 4.0.325008.5.
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_sx$2$(not in LMFDB)