# Properties

 Label 2.113.abj_uk 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: $( 1 - 19 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$ Frobenius angles: $\pm0.148111132014$, $\pm0.228810695365$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=10x^6+29x^5+66x^4+32x^3+6x^2+81x+3$
• $y^2=74x^6+100x^5+21x^4+65x^3+58x^2+58x+82$
• $y^2=55x^6+63x^5+45x^4+14x^3+12x^2+106x+47$
• $y^2=87x^6+48x^5+87x^4+16x^3+80x^2+19x+89$
• $y^2=44x^6+19x^5+66x^4+33x^3+112x^2+37x+55$
• $y^2=39x^6+15x^5+39x^4+89x^3+55x^2+49x+73$
• $y^2=48x^6+68x^5+34x^4+5x^3+6x^2+73x+20$
• $y^2=111x^6+24x^5+94x^4+70x^3+35x^2+55x+40$
• $y^2=62x^6+6x^5+103x^4+50x^3+42x^2+55x+34$
• $y^2=15x^6+15x^5+59x^4+17x^3+66x^2+104x+48$
• $y^2=52x^6+53x^5+82x^4+49x^3+48x^2+31x+58$
• $y^2=37x^6+95x^5+35x^4+19x^3+103x^2+10x+18$
• $y^2=26x^6+72x^5+86x^4+93x^3+112x^2+16x+41$
• $y^2=5x^6+45x^5+26x^4+30x^3+23x+27$
• $y^2=23x^6+103x^5+17x^4+5x^3+17x^2+111x+6$
• $y^2=75x^6+30x^5+29x^4+53x^3+9x^2+12x+69$
• $y^2=39x^6+107x^5+112x^4+26x^3+93x^2+2x+111$
• $y^2=29x^6+52x^5+85x^4+12x^3+63x+93$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9310 160969900 2083267120480 26589651961600000 339464667533711745550 4334531080902907276537600 55347530368934151536407770670 706732552458568825561930521600000 9024267960151216182412493894174393440 115230877640250356714979121954014471947500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 79 12605 1443808 163079313 18424782119 2081955585890 235260568883783 26584441920742753 3004041936314164384 339456738971650064525

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.at $\times$ 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.ad_ada $2$ (not in LMFDB) 2.113.d_ada $2$ (not in LMFDB) 2.113.bj_uk $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.ad_ada $2$ (not in LMFDB) 2.113.d_ada $2$ (not in LMFDB) 2.113.bj_uk $2$ (not in LMFDB) 2.113.abh_sy $4$ (not in LMFDB) 2.113.af_abo $4$ (not in LMFDB) 2.113.f_abo $4$ (not in LMFDB) 2.113.bh_sy $4$ (not in LMFDB)