Properties

Label 2.113.abj_ue
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:  $1 - 35 x + 524 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0923236320190$, $\pm0.258475729173$
Angle rank:  $2$ (numerical)
Number field:  4.0.2395800.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9304 160810336 2082355817056 26586920153147776 339459173341170922264 4334523157682478998265856 55347522706658027728354221016 706732550112991618606304845555200 9024267968741467354633576704643656544 115230877662671774754530891327811008857696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12593 1443178 163062561 18424483919 2081951780222 235260536314463 26584441832511553 3004041939173728714 339456739037700949553

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.2395800.1.
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.bj_ue$2$(not in LMFDB)