Properties

Label 2.113.abm_wp
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:  $( 1 - 19 x + 113 x^{2} )^{2}$
Frobenius angles:  $\pm0.148111132014$, $\pm0.148111132014$
Angle rank:  $1$ (numerical)
Jacobians:  9

This isogeny class is not 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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9025 159643225 2080748550400 26586827039355625 339463599592217100625 4334534388837076439142400 55347539804010012966393723025 706732567174415384576749292855625 9024267975600464058067191963677190400 115230877648717401706345005987418741005625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12500 1442062 163061988 18424724156 2081957174750 235260608988572 26584442474293828 3004041941456984686 339456738996592992500

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.at 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-91}) \)$)$
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_aff$2$(not in LMFDB)
2.113.bm_wp$2$(not in LMFDB)
2.113.t_jo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_aff$2$(not in LMFDB)
2.113.bm_wp$2$(not in LMFDB)
2.113.t_jo$3$(not in LMFDB)
2.113.a_ff$4$(not in LMFDB)
2.113.at_jo$6$(not in LMFDB)