# Properties

 Label 2.113.abk_va 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: $( 1 - 20 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$ Frobenius angles: $\pm0.110150159186$, $\pm0.228810695365$ 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:

• $y^2=71x^6+98x^5+108x^4+40x^3+27x^2+105x+17$
• $y^2=70x^6+58x^5+20x^4+78x^3+68x^2+110x+89$
• $y^2=104x^6+56x^5+43x^4+95x^3+51x^2+19x+79$
• $y^2=27x^6+105x^5+84x^4+63x^3+73x^2+7x+7$
• $y^2=87x^6+25x^5+54x^4+71x^3+54x^2+25x+87$
• $y^2=42x^6+52x^5+85x^4+101x^3+17x^2+71x+16$
• $y^2=34x^6+88x^5+48x^4+37x^3+5x^2+90x+110$
• $y^2=17x^6+90x^5+76x^4+73x^3+11x^2+33x+52$
• $y^2=62x^6+48x^5+93x^4+29x^3+102x^2+19x+10$
• $y^2=35x^6+103x^5+106x^4+41x^3+77x^2+33x+84$
• $y^2=40x^6+68x^5+24x^4+93x^3+24x^2+68x+40$
• $y^2=97x^6+66x^5+82x^4+106x^3+16x^2+x+5$
• $y^2=75x^6+43x^5+66x^4+51x^3+66x^2+43x+75$
• $y^2=77x^6+21x^5+9x^4+107x^3+41x^2+47x+96$
• $y^2=80x^6+75x^5+100x^4+9x^3+52x^2+70x+78$
• $y^2=84x^6+61x^5+9x^4+19x^3+17x^2+85x+66$
• $y^2=49x^6+96x^5+68x^4+63x^3+84x^2+107x+98$
• $y^2=17x^6+15x^5+54x^4+8x^3+54x^2+15x+17$
• $y^2=70x^6+90x^5+99x^4+83x^3+99x^2+90x+70$
• $y^2=88x^6+110x^5+66x^4+81x^3+9x^2+28x+3$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9212 160473040 2082108851228 26587686780928000 339462031324100340572 4334528345891382494499280 55347528629347858138866470588 706732553283519274288526131200000 9024267965344594308033001649810310332 115230877651386491245580173612768806005200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12566 1443006 163067262 18424639038 2081954272214 235260561489486 26584441951774078 3004041938042961198 339456739004455819286

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.au $\times$ 1.113.aq 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.ae_adq $2$ (not in LMFDB) 2.113.e_adq $2$ (not in LMFDB) 2.113.bk_va $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.ae_adq $2$ (not in LMFDB) 2.113.e_adq $2$ (not in LMFDB) 2.113.bk_va $2$ (not in LMFDB) 2.113.abi_tm $4$ (not in LMFDB) 2.113.ag_acc $4$ (not in LMFDB) 2.113.g_acc $4$ (not in LMFDB) 2.113.bi_tm $4$ (not in LMFDB)