# Properties

 Label 2.113.abl_vq 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: $( 1 - 21 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.228810695365$ Angle rank: $2$ (numerical) Jacobians: 9

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 9 curves, and hence is principally polarizable:

• $y^2=84x^6+17x^5+25x^4+81x^3+110x^2+11x+106$
• $y^2=79x^6+102x^5+6x^4+88x^3+40x^2+78x+13$
• $y^2=82x^6+10x^5+28x^4+45x^3+9x^2+82x+48$
• $y^2=43x^6+102x^5+46x^4+23x^3+49x^2+59x+47$
• $y^2=89x^6+81x^5+23x^4+4x^3+37x^2+93x+49$
• $y^2=92x^6+85x^5+34x^4+67x^3+32x^2+73x+27$
• $y^2=7x^6+32x^5+18x^4+102x^3+104x^2+16x+79$
• $y^2=23x^6+85x^5+82x^4+16x^3+9x^2+9x+112$
• $y^2=108x^6+38x^5+89x^4+102x^3+81x^2+108x+50$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9114 159950700 2080777274856 26585085945600000 339457692681824264394 4334521892328811430956800 55347519903935137138188406506 706732542503439792704142105600000 9024267953265503348608310378133973224 115230877639453623098469019219973722867500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 77 12525 1442084 163051313 18424403557 2081951172450 235260524401189 26584441546270753 3004041934022015012 339456738969302980125

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 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.af_aeg $2$ (not in LMFDB) 2.113.f_aeg $2$ (not in LMFDB) 2.113.bl_vq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.113.af_aeg $2$ (not in LMFDB) 2.113.f_aeg $2$ (not in LMFDB) 2.113.bl_vq $2$ (not in LMFDB) 2.113.abj_ua $4$ (not in LMFDB) 2.113.ah_acq $4$ (not in LMFDB) 2.113.h_acq $4$ (not in LMFDB) 2.113.bj_ua $4$ (not in LMFDB)