# Properties

 Label 2.163.abs_bfe Base Field $\F_{163}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{163}$ Dimension: $2$ L-polynomial: $( 1 - 22 x + 163 x^{2} )^{2}$ Frobenius angles: $\pm0.169471200781$, $\pm0.169471200781$ Angle rank: $1$ (numerical) Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=116x^6+154x^5+28x^4+57x^3+28x^2+154x+116$
• $y^2=36x^6+135x^5+117x^4+122x^3+16x^2+20x+114$
• $y^2=129x^6+15x^4+15x^2+129$
• $y^2=63x^6+78x^5+28x^4+160x^3+2x^2+32x+52$
• $y^2=70x^6+49x^5+95x^4+144x^3+7x^2+67x+127$
• $y^2=115x^6+79x^5+89x^4+77x^3+89x^2+79x+115$
• $y^2=68x^6+71x^5+157x^4+82x^3+23x^2+116x+39$
• $y^2=47x^6+57x^5+145x^4+67x^3+55x^2+96x+46$
• $y^2=80x^6+97x^4+97x^2+80$
• $y^2=156x^6+71x^5+41x^4+7x^3+41x^2+71x+156$
• $y^2=97x^6+132x^5+13x^4+34x^3+13x^2+132x+97$
• $y^2=33x^6+25x^5+9x^4+103x^3+9x^2+25x+33$
• $y^2=127x^6+38x^5+50x^4+43x^3+45x^2+121x+10$
• $y^2=117x^6+112x^5+48x^4+81x^3+106x^2+58x+98$
• $y^2=114x^6+130x^5+94x^4+30x^3+130x^2+54x+52$
• $y^2=55x^6+155x^5+105x^4+36x^3+105x^2+155x+55$
• $y^2=71x^6+74x^5+61x^4+89x^3+150x^2+72x+32$
• $y^2=75x^6+29x^5+32x^4+x^3+162x^2+126x+24$
• $y^2=2x^6+66x^3+154$
• $y^2=90x^6+45x^5+13x^4+16x^3+92x^2+162x+119$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20164 697593744 18756331016164 498351193239684096 13239774480732511599364 351764212452980009136579216 9346015304071806209233753988644 248314266255688156522375661921255424 6597461723549936594946605249687625801796 175287960535661549493786405009143859510363024

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 120 26254 4330968 705968110 115064820840 18755386876798 3057125425570056 498311415554219614 81224760530998111704 13239635966753852127214

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.aw 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-42})$$$)$
All geometric endomorphisms are defined over $\F_{163}$.

## 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 2.163.a_agc $2$ (not in LMFDB) 2.163.bs_bfe $2$ (not in LMFDB) 2.163.w_mj $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.a_agc $2$ (not in LMFDB) 2.163.bs_bfe $2$ (not in LMFDB) 2.163.w_mj $3$ (not in LMFDB) 2.163.a_gc $4$ (not in LMFDB) 2.163.aw_mj $6$ (not in LMFDB)