# Properties

 Label 2.113.abl_vs 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: $1 - 37 x + 564 x^{2} - 4181 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.0818341620435$, $\pm0.218655119859$ Angle rank: $2$ (numerical) Number field: 4.0.95948.1 Galois group: $D_{4}$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

• $y^2=80x^6+11x^5+98x^4+49x^3+96x^2+98x+7$
• $y^2=15x^6+19x^5+12x^4+42x^3+93x^2+44x+56$
• $y^2=78x^6+20x^5+63x^4+22x^3+107x^2+50x+76$
• $y^2=15x^6+3x^5+68x^4+16x^3+96x^2+66x+42$
• $y^2=28x^6+49x^5+61x^4+33x^3+68x^2+52x+71$
• $y^2=73x^6+65x^5+93x^4+18x^3+106x^2+55x+83$
• $y^2=67x^6+12x^5+65x^4+28x^3+66x^2+79x+10$
• $y^2=78x^6+48x^5+81x^4+61x^3+23x^2+59x+101$
• $y^2=79x^6+101x^5+49x^4+24x^3+32x^2+98x+6$
• $y^2=31x^6+46x^5+83x^4+38x^3+82x^2+23x+63$
• $y^2=74x^6+31x^5+98x^4+71x^3+33x^2+19x+43$
• $y^2=86x^6+17x^5+5x^4+x^3+23x^2+95x+31$
• $y^2=3x^6+43x^5+29x^4+24x^3+61x^2+12x+54$
• $y^2=90x^6+4x^5+87x^4+83x^3+70x^2+35x+112$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9116 160004032 2081098495232 26586137473781504 339460119564550357276 4334526277279077469339648 55347526411036593416015935772 706732550613126249125301192768512 9024267961852569805291059807871016192 115230877647338853939723990822387235099072

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 77 12529 1442306 163057761 18424535277 2081953278622 235260552060317 26584441851324609 3004041936880519202 339456738992531951409

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.95948.1.
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.bl_vs $2$ (not in LMFDB)