Properties

Label 2.113.abm_wn
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:  $1 - 38 x + 585 x^{2} - 4294 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0901024562033$, $\pm0.189951722793$
Angle rank:  $2$ (numerical)
Number field:  4.0.322112.1
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
$A(\F_{q^r})$ 9023 159589801 2080418564924 26585707627025561 339460904063616474223 4334529303322089961478032 55347532027779581185283991359 706732557688997102055936973211753 9024267967426691635383444238744878908 115230877647252001857676911156101167478041

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12496 1441834 163055124 18424577856 2081954732086 235260575934880 26584442117490468 3004041938736059818 339456738992276095296

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.322112.1.
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_wn$2$(not in LMFDB)