Properties

Label 2.113.abl_vv
Base field $\F_{113}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 37 x + 567 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.125932323751$, $\pm0.195315764367$
Angle rank:  $2$ (numerical)
Number field:  4.0.251525.1
Galois group:  $D_{4}$
Jacobians:  11

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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9119 160084045 2081580351191 26587709893247525 339463708769380319344 4334532575673493601124805 55347535113292175299156359551 706732559654515008153553485743525 9024267967138072773892549595512288799 115230877643442455480000794885904731168000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12535 1442639 163067403 18424730082 2081956303855 235260589050179 26584442191425363 3004041938639982977 339456738981053615550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.251525.1.
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_vv$2$(not in LMFDB)