# Properties

 Label 2.113.abk_vb 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: $1 - 36 x + 547 x^{2} - 4068 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.121426339854$, $\pm0.222649971582$ Angle rank: $2$ (numerical) Number field: 4.0.13968.2 Galois group: $D_{4}$ Jacobians: 22

This isogeny class is simple and geometrically 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 22 curves, and hence is principally polarizable:

• $y^2=101x^6+103x^5+85x^4+37x^3+97x^2+110x+61$
• $y^2=46x^6+28x^5+44x^3+76x^2+41x+39$
• $y^2=54x^6+2x^5+38x^4+57x^3+31x^2+77x+75$
• $y^2=75x^6+73x^5+46x^4+22x^3+2x^2+88x+69$
• $y^2=10x^6+18x^5+78x^4+29x^3+46x^2+56x+69$
• $y^2=43x^6+88x^5+53x^3+111x^2+97x+20$
• $y^2=41x^6+11x^5+95x^4+108x^3+89x^2+50x+54$
• $y^2=108x^6+18x^5+61x^4+67x^3+87x^2+29x+64$
• $y^2=108x^6+58x^5+65x^4+43x^3+99x^2+26x+69$
• $y^2=16x^6+101x^5+107x^4+58x^3+30x^2+26x+108$
• $y^2=20x^6+110x^5+19x^4+9x^3+83x^2+32x+88$
• $y^2=107x^6+80x^5+80x^4+54x^3+80x^2+112x+59$
• $y^2=85x^6+38x^5+x^4+27x^3+97x^2+18x+91$
• $y^2=107x^6+58x^5+27x^4+52x^3+103x^2+7x+12$
• $y^2=53x^6+82x^5+65x^4+38x^3+66x^2+38x+21$
• $y^2=96x^6+110x^5+42x^4+55x^3+x^2+43x+29$
• $y^2=61x^6+36x^5+96x^4+10x^2+53x+29$
• $y^2=15x^6+100x^5+29x^4+87x^3+x^2+37x+94$
• $y^2=73x^6+26x^5+111x^4+35x^3+80x^2+23x+55$
• $y^2=84x^6+78x^5+85x^4+42x^3+77x^2+69x+23$
• $y^2=111x^6+53x^5+84x^4+59x^3+44x^2+29x+26$
• $y^2=18x^6+11x^5+55x^4+11x^3+38x^2+63x+4$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9213 160499673 2082265102548 26588175686087769 339463079313521825013 4334530014951596472719376 55347530576526081962459706309 706732554613501210707895190746473 9024267964729274800021421393739701652 115230877647540674372615399922261032330313

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 78 12568 1443114 163070260 18424695918 2081955073894 235260569766174 26584442001802660 3004041937838130666 339456738993126490888

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.13968.2.
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.bk_vb $2$ (not in LMFDB)