Properties

Label 2.113.abl_vs
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:  $1 - 37 x + 564 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0818341620435$, $\pm0.218655119859$
Angle rank:  $2$ (numerical)
Number field:  4.0.95948.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9116 160004032 2081098495232 26586137473781504 339460119564550357276 4334526277279077469339648 55347526411036593416015935772 706732550613126249125301192768512 9024267961852569805291059807871016192 115230877647338853939723990822387235099072

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12529 1442306 163057761 18424535277 2081953278622 235260552060317 26584441851324609 3004041936880519202 339456738992531951409

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.95948.1.
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.bl_vs$2$(not in LMFDB)