# Properties

 Label 2.113.abj_uf 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: $1 - 35 x + 525 x^{2} - 3955 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.101307485312$, $\pm0.254747453785$ Angle rank: $2$ (numerical) Number field: 4.0.8663141.1 Galois group: $D_{4}$ Jacobians: 27

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 27 curves, and hence is principally polarizable:

• $y^2=x^6+10x^5+93x^4+88x^3+104x^2+5x+84$
• $y^2=90x^6+34x^5+47x^4+112x^3+93x^2+58x+39$
• $y^2=89x^6+78x^5+63x^4+4x^3+24x^2+6x+38$
• $y^2=73x^6+60x^5+35x^4+22x^3+58x^2+20x+6$
• $y^2=101x^6+51x^5+54x^4+23x^3+14x^2+32x+67$
• $y^2=42x^6+58x^5+112x^4+23x^3+60x^2+45x+60$
• $y^2=80x^6+76x^5+95x^4+57x^3+104x^2+x+32$
• $y^2=86x^6+106x^5+34x^4+44x^3+4x^2+58x+93$
• $y^2=11x^6+67x^5+15x^4+34x^3+99x^2+91x+88$
• $y^2=77x^6+8x^5+25x^4+80x^3+42x^2+52x+72$
• $y^2=93x^6+37x^5+24x^4+109x^3+14x^2+14x+82$
• $y^2=75x^6+98x^5+25x^4+39x^3+45x^2+85x+89$
• $y^2=77x^6+21x^5+21x^4+111x^3+98x^2+28x+18$
• $y^2=47x^6+93x^5+45x^4+14x^3+16x^2+10x+112$
• $y^2=36x^6+48x^5+43x^4+86x^3+81x^2+34x+5$
• $y^2=20x^6+12x^5+30x^4+83x^3+111x^2+111x+21$
• $y^2=39x^6+40x^5+20x^4+20x^3+108x^2+71x+71$
• $y^2=68x^6+49x^5+59x^4+59x^3+18x^2+106x+38$
• $y^2=90x^6+23x^5+94x^4+37x^3+65x^2+99x+7$
• $y^2=64x^6+71x^5+82x^4+103x^3+54x^2+3x+48$
• $y^2=82x^6+32x^5+5x^4+4x^3+72x^2+31x+55$
• $y^2=3x^6+5x^5+26x^4+94x^3+67x^2+40x+24$
• $y^2=88x^6+40x^5+29x^4+102x^3+77x^2+80x+39$
• $y^2=3x^6+4x^5+32x^4+4x^3+95x^2+27x+95$
• $y^2=112x^6+100x^5+65x^4+37x^3+96x^2+6x+101$
• $y^2=94x^6+104x^5+85x^3+10x^2+81x+47$
• $y^2=58x^6+76x^5+19x^4+18x^3+3x^2+78x+53$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9305 160836925 2082507693065 26587377079743125 339460105159131270400 4334524560112221010269325 55347524267287002563076892385 706732551249414021036375741993125 9024267968872428095665975350510830945 115230877661590421325689788664051653120000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 79 12595 1443283 163065363 18424534494 2081952453835 235260542948083 26584441875259203 3004041939217323559 339456739034515408350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.8663141.1.
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.
 Twist Extension Degree Common base change 2.113.bj_uf $2$ (not in LMFDB)