# Properties

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

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## Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $( 1 - 18 x + 113 x^{2} )^{2}$ Frobenius angles: $\pm0.178616545187$, $\pm0.178616545187$ Angle rank: $1$ (numerical) Jacobians: 46

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 46 curves, and hence is principally polarizable:

• $y^2=47x^6+93x^5+42x^4+61x^3+12x^2+86x+94$
• $y^2=59x^6+68x^4+68x^2+59$
• $y^2=21x^6+110x^5+31x^4+45x^3+31x^2+110x+21$
• $y^2=61x^6+89x^5+89x^4+112x^3+89x^2+89x+61$
• $y^2=20x^6+6x^5+92x^4+84x^3+78x^2+92x+34$
• $y^2=10x^6+102x^5+10x^4+45x^3+103x^2+102x+103$
• $y^2=47x^6+15x^4+15x^2+47$
• $y^2=92x^6+78x^5+10x^4+36x^3+10x^2+78x+92$
• $y^2=67x^6+34x^5+62x^4+100x^3+62x^2+34x+67$
• $y^2=32x^6+81x^5+109x^4+20x^3+109x^2+81x+32$
• $y^2=8x^6+57x^5+87x^4+22x^3+87x^2+57x+8$
• $y^2=108x^6+33x^5+57x^4+53x^3+57x^2+33x+108$
• $y^2=52x^6+90x^5+15x^4+88x^3+15x^2+90x+52$
• $y^2=103x^6+69x^5+54x^4+47x^3+34x^2+52x+55$
• $y^2=102x^6+71x^5+94x^4+92x^3+94x^2+71x+102$
• $y^2=108x^6+31x^5+58x^4+85x^3+58x^2+31x+108$
• $y^2=30x^6+100x^4+100x^2+30$
• $y^2=7x^6+101x^5+56x^4+37x^3+55x^2+2x+75$
• $y^2=43x^6+22x^5+94x^4+94x^3+101x^2+24x$
• $y^2=97x^6+78x^5+21x^4+88x^3+107x^2+94x+32$
• and 26 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9216 160579584 2082733876224 26589638502383616 339466183491188745216 4334534812822949426774016 55347535662524742615108166656 706732556518712387337796498489344 9024267958264608008618500785583727616 115230877627652515305272763087380269645824

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12574 1443438 163079230 18424864398 2081957378398 235260591384750 26584442073469054 3004041935686141134 339456738934538291614

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-2})$$$)$
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.a_adu $2$ (not in LMFDB) 2.113.bk_ve $2$ (not in LMFDB) 2.113.s_id $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.a_adu $2$ (not in LMFDB) 2.113.bk_ve $2$ (not in LMFDB) 2.113.s_id $3$ (not in LMFDB) 2.113.a_du $4$ (not in LMFDB) 2.113.as_id $6$ (not in LMFDB) 2.113.aq_ey $8$ (not in LMFDB) 2.113.q_ey $8$ (not in LMFDB)