# Properties

 Label 2.113.abm_wk 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: $1 - 38 x + 582 x^{2} - 4294 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.0151964286034$, $\pm0.210853355850$ Angle rank: $2$ (numerical) Number field: 4.0.4400.1 Galois group: $D_{4}$ Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=44x^6+51x^5+53x^4+71x^3+20x^2+24x+5$
• $y^2=46x^6+15x^5+105x^4+37x^3+83x^2+112x+66$
• $y^2=102x^6+84x^5+11x^4+23x^3+88x^2+9x+96$
• $y^2=37x^6+2x^5+53x^4+16x^3+54x^2+31x+33$
• $y^2=24x^6+101x^5+72x^4+3x^3+73x^2+92x+84$
• $y^2=46x^6+105x^5+14x^4+3x^3+103x^2+46x+10$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9020 159509680 2079923613020 26584023637318400 339456808270912865500 4334521378749489394991920 55347519192888865718192533820 706732539834360918602977162342400 9024267945821559123211229992401868220 115230877624335369116273262703055750782000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 76 12490 1441492 163044798 18424355556 2081950925770 235260521378812 26584441445870718 3004041931544038876 339456738924766365450

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.4400.1.
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.bm_wk $2$ (not in LMFDB)