# 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:

• $y^2=77x^6+92x^5+104x^4+42x^3+4x^2+67x+105$
• $y^2=56x^6+90x^5+27x^4+55x^3+108x^2+84x+81$
• $y^2=47x^6+44x^5+21x^4+5x^3+40x^2+15x+66$
• $y^2=35x^6+58x^5+45x^4+8x^3+2x^2+77x+98$
• $y^2=29x^6+99x^5+67x^4+86x^3+83x^2+38x+31$
• $y^2=93x^6+9x^5+102x^4+79x^3+51x^2+87x+54$
• $y^2=41x^6+106x^5+24x^4+85x^3+45x^2+16x+18$
• $y^2=72x^6+103x^5+4x^4+24x^3+87x^2+86x+2$
• $y^2=60x^6+14x^5+96x^4+102x^3+93x^2+53$

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)