# Properties

 Label 2.113.abj_ua 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: $( 1 - 21 x + 113 x^{2} )( 1 - 14 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.271189304635$ Angle rank: $2$ (numerical) Jacobians: 30

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 30 curves, and hence is principally polarizable:

• $y^2=76x^6+11x^5+24x^4+5x^3+35x^2+62x+95$
• $y^2=82x^6+20x^5+57x^4+30x^3+45x^2+9x+61$
• $y^2=47x^6+85x^5+46x^4+31x^3+90x^2+102x+75$
• $y^2=23x^6+22x^5+3x^4+40x^3+6x^2+43x+99$
• $y^2=99x^6+91x^5+44x^4+8x^3+2x^2+55x+63$
• $y^2=23x^6+64x^5+7x^4+57x^3+62x^2+96x+35$
• $y^2=71x^6+95x^5+23x^4+17x^3+37x^2+101x+78$
• $y^2=25x^6+112x^5+4x^4+27x^3+17x^2+89x+41$
• $y^2=38x^6+102x^5+68x^4+102x^3+41x^2+40x+19$
• $y^2=76x^6+104x^5+4x^4+98x^3+25x^2+37x+14$
• $y^2=98x^6+52x^5+15x^4+19x^3+97x^2+103x+32$
• $y^2=58x^6+103x^5+110x^4+41x^3+94x^2+81x+56$
• $y^2=25x^6+104x^5+26x^3+53x^2+35x+41$
• $y^2=29x^6+23x^5+108x^4+6x^3+6x^2+10x+29$
• $y^2=56x^6+96x^5+70x^4+65x^3+93x^2+12x+28$
• $y^2=95x^6+91x^5+83x^4+66x^3+17x^2+29x+45$
• $y^2=23x^6+60x^5+71x^4+88x^3+11x^2+55x+65$
• $y^2=21x^6+86x^5+74x^3+9x^2+6x+20$
• $y^2=72x^6+22x^5+38x^4+83x^3+16x^2+85x+58$
• $y^2=24x^6+56x^5+25x^4+72x^3+36x^2+38x+91$
• $y^2=87x^6+60x^5+54x^4+90x^3+30x^2+54x+76$
• $y^2=51x^6+58x^5+106x^4+100x^3+87x^2+12x+1$
• $y^2=80x^6+68x^5+32x^4+28x^3+93x^2+50x+111$
• $y^2=103x^6+5x^5+90x^4+58x^3+44x^2+107x+23$
• $y^2=8x^6+26x^5+72x^4+16x^3+110x^2+16x+57$
• $y^2=97x^6+107x^5+70x^4+59x^3+50x^2+76x+76$
• $y^2=40x^6+8x^5+32x^4+32x^3+58x^2+103x+47$
• $y^2=72x^6+81x^5+101x^4+12x^3+10x^2+83x+45$
• $y^2=101x^6+92x^5+36x^4+17x^3+58x^2+64x+49$
• $y^2=3x^6+27x^5+8x^4+50x^3+103x^2+52x+17$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9300 160704000 2081748344400 26585085945600000 339455381592115816500 4334517219558479671296000 55347515318282448289094330100 706732542503439792704142105600000 9024267961570017235282993028796613200 115230877654904057098829218314924849600000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 79 12585 1442758 163051313 18424278119 2081948928030 235260504909383 26584441546270753 3004041936786461734 339456739014818158425

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 1.113.ao and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ah_acq $2$ (not in LMFDB) 2.113.h_acq $2$ (not in LMFDB) 2.113.bj_ua $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.ah_acq $2$ (not in LMFDB) 2.113.h_acq $2$ (not in LMFDB) 2.113.bj_ua $2$ (not in LMFDB) 2.113.abl_vq $4$ (not in LMFDB) 2.113.af_aeg $4$ (not in LMFDB) 2.113.f_aeg $4$ (not in LMFDB) 2.113.bl_vq $4$ (not in LMFDB)