# Properties

 Label 2.113.abk_uv 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: $( 1 - 21 x + 113 x^{2} )( 1 - 15 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.250704227710$ Angle rank: $2$ (numerical) Jacobians: 35

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 35 curves, and hence is principally polarizable:

• $y^2=19x^6+76x^5+8x^4+92x^3+3x^2+75x+60$
• $y^2=12x^6+109x^5+37x^4+71x^3+96x^2+69x+93$
• $y^2=17x^6+74x^5+22x^4+101x^3+90x^2+16x+26$
• $y^2=45x^6+9x^5+16x^4+64x^3+16x^2+9x+45$
• $y^2=21x^6+35x^5+40x^4+109x^3+40x^2+35x+21$
• $y^2=29x^6+63x^5+68x^4+80x^3+68x^2+63x+29$
• $y^2=95x^6+79x^5+15x^4+77x^3+18x^2+7x+90$
• $y^2=5x^6+31x^5+87x^4+106x^3+107x^2+22x+5$
• $y^2=76x^6+25x^5+92x^4+49x^3+76x^2+70x+54$
• $y^2=5x^6+12x^5+72x^4+20x^3+79x^2+83x+89$
• $y^2=5x^6+83x^5+110x^4+87x^3+110x^2+83x+5$
• $y^2=73x^6+101x^5+89x^4+70x^3+9x^2+18x+98$
• $y^2=27x^6+10x^5+20x^4+110x^3+111x^2+67x+66$
• $y^2=4x^6+105x^5+25x^4+99x^3+19x^2+59x+23$
• $y^2=43x^6+92x^5+13x^4+29x^3+13x^2+92x+43$
• $y^2=5x^6+97x^5+33x^4+110x^3+10x^2+79x+101$
• $y^2=28x^6+30x^5+101x^4+33x^3+101x^2+30x+28$
• $y^2=24x^6+94x^5+7x^4+85x^3+92x^2+111x+21$
• $y^2=3x^6+39x^5+5x^4+73x^3+5x^2+39x+3$
• $y^2=69x^6+42x^5+46x^4+14x^3+46x^2+42x+69$
• and 15 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9207 160339905 2081327643648 26585232506580825 339456691899909109647 4334519476192466926632960 55347516988609419659410122303 706732541304286735260718731275625 9024267956283398383374651784318835712 115230877647455556053704680937196533607025

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12556 1442466 163052212 18424349238 2081950011934 235260512009286 26584441501163428 3004041935026626498 339456738992875742236

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 1.113.ap 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.ag_adl $2$ (not in LMFDB) 2.113.g_adl $2$ (not in LMFDB) 2.113.bk_uv $2$ (not in LMFDB)