Properties

Label 2.113.abm_wm
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 38 x + 584 x^{2} - 4294 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0711049505690$, $\pm0.198261056171$
Angle rank:  $2$ (numerical)
Number field:  4.0.491328.3
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9022 159563092 2080253577454 26585146946632144 339459545799370847422 4334526701329566455428468 55347527905930832794640959918 706732552223925599461195605537792 9024267961486865896833550243072064398 115230877642442984986862668605825016427572

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12494 1441720 163051686 18424504136 2081953482302 235260558414524 26584441911916414 3004041936758781916 339456738978109291934

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.491328.3.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.bm_wm$2$(not in LMFDB)