# Properties

 Label 2.113.abk_uy Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $1 - 36 x + 544 x^{2} - 4068 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.0881917305060$, $\pm0.238851186738$ Angle rank: $2$ (numerical) Number field: 4.0.4094208.2 Galois group: $D_{4}$ Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=49x^6+35x^5+71x^4+92x^3+110x^2+57x+93$
• $y^2=27x^6+70x^5+18x^4+73x^3+73x^2+50x+93$
• $y^2=73x^6+38x^5+38x^4+105x^3+64x^2+39x+19$
• $y^2=13x^6+61x^5+51x^4+80x^3+87x^2+39x+63$
• $y^2=72x^6+91x^5+98x^4+21x^3+71x^2+58x+81$
• $y^2=47x^6+13x^5+17x^4+7x^3+84x^2+10x+42$
• $y^2=67x^6+109x^5+101x^4+15x^3+76x^2+22x+41$
• $y^2=40x^6+87x^5+94x^4+49x^3+45x^2+111x+47$
• $y^2=33x^6+22x^5+26x^4+104x^3+105x^2+62x+35$
• $y^2=101x^6+56x^5+61x^4+106x^3+59x^2+32x+61$
• $y^2=89x^6+28x^5+32x^4+83x^3+12x^2+48x+65$
• $y^2=3x^6+81x^5+99x^4+31x^3+35x^2+75x+105$
• $y^2=92x^6+104x^5+27x^4+78x^3+12x^2+8x+92$
• $y^2=75x^6+35x^5+64x^4+58x^3+10x^2+108x+25$
• $y^2=19x^6+26x^5+12x^4+45x^3+74x+2$
• $y^2=21x^6+72x^4+45x^3+87x^2+29x+108$
• $y^2=96x^6+71x^5+101x^3+81x^2+12x+50$
• $y^2=21x^6+24x^5+x^4+36x^3+19x^2+103x+88$
• $y^2=32x^6+41x^5+69x^4+18x^3+73x^2+13x+104$
• $y^2=17x^6+23x^5+64x^4+35x^3+107x^2+70x+112$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9210 160419780 2081796358410 26586707020938000 339459915449879647050 4334524902966359905318980 55347524355089099129868254010 706732549565528990476812036096000 9024267964187181268217615100278631930 115230877654599325445327437268869244280900

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12562 1442790 163061254 18424524198 2081952618514 235260543321294 26584441811918206 3004041937657675950 339456739013920454482

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.4094208.2.
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.
 Twist Extension Degree Common base change 2.113.bk_uy $2$ (not in LMFDB)