Properties

Label 2.113.abk_vb
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:  $1 - 36 x + 547 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.121426339854$, $\pm0.222649971582$
Angle rank:  $2$ (numerical)
Number field:  4.0.13968.2
Galois group:  $D_{4}$
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9213 160499673 2082265102548 26588175686087769 339463079313521825013 4334530014951596472719376 55347530576526081962459706309 706732554613501210707895190746473 9024267964729274800021421393739701652 115230877647540674372615399922261032330313

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12568 1443114 163070260 18424695918 2081955073894 235260569766174 26584442001802660 3004041937838130666 339456738993126490888

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.13968.2.
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.bk_vb$2$(not in LMFDB)