# Properties

 Label 2.113.abi_tf 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: $( 1 - 21 x + 113 x^{2} )( 1 - 13 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.290579079721$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=67x^6+69x^5+51x^4+13x^3+44x^2+44x+70$
• $y^2=38x^6+12x^5+22x^4+55x^3+52x^2+110x+70$
• $y^2=3x^6+30x^5+84x^4+87x^3+3x^2+78x+55$
• $y^2=4x^6+19x^5+72x^4+12x^3+47x^2+33x+90$
• $y^2=82x^6+60x^5+19x^4+8x^3+28x^2+74x+2$
• $y^2=107x^6+79x^5+80x^4+57x^3+47x^2+90x+65$
• $y^2=54x^6+78x^5+67x^4+38x^3+3x^2+83x+72$
• $y^2=20x^6+54x^5+77x^4+70x^3+89x^2+103x+87$
• $y^2=63x^6+18x^5+104x^4+54x^3+72x^2+64x+64$
• $y^2=73x^6+16x^5+83x^4+12x^3+59x^2+109x+96$
• $y^2=53x^6+19x^5+16x^4+92x^3+52x^2+69x+101$
• $y^2=80x^6+8x^5+96x^4+18x^3+6x^2+77x+21$
• $y^2=53x^6+79x^5+57x^4+93x^3+13x^2+25x+67$
• $y^2=30x^6+54x^5+91x^4+17x^3+27x^2+11x+34$
• $y^2=47x^6+45x^5+95x^4+86x^3+44x^2+63x+104$
• $y^2=86x^6+18x^5+50x^4+78x^3+74x^2+102x+9$
• $y^2=84x^6+97x^5+100x^4+59x^3+22x^2+103x+43$
• $y^2=71x^6+10x^5+98x^4+4x^3+72x^2+27x+20$
• $y^2=19x^6+87x^5+58x^4+75x^3+70x^2+41x+65$
• $y^2=109x^6+5x^5+106x^4+92x^3+51x^2+74x+102$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9393 161042985 2082048021648 26584702995940425 339453931997677361073 4334515395570368456232960 55347514994490787432086748689 706732545433883303422080819225225 9024267967185981305072542180530221712 115230877659143516597630244605140391152425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 80 12612 1442966 163048964 18424199440 2081948051934 235260503533072 26584441656502276 3004041938655930998 339456739027307112132

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 1.113.an 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.ai_abv $2$ (not in LMFDB) 2.113.i_abv $2$ (not in LMFDB) 2.113.bi_tf $2$ (not in LMFDB)