# Properties

 Label 2.163.abw_bir 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: $( 1 - 25 x + 163 x^{2} )( 1 - 23 x + 163 x^{2} )$ Frobenius angles: $\pm0.0652307277549$, $\pm0.143017980409$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=32x^6+16x^5+68x^4+36x^3+162x^2+22x+124$
• $y^2=35x^6+88x^5+59x^4+94x^3+48x^2+39x+41$
• $y^2=137x^6+154x^5+4x^4+161x^3+40x^2+78x+80$
• $y^2=72x^6+125x^5+47x^4+88x^3+26x^2+142x+89$
• $y^2=96x^6+33x^5+25x^4+97x^3+151x^2+150x+161$
• $y^2=48x^6+26x^5+35x^4+86x^3+131x^2+22x+123$
• $y^2=6x^6+159x^5+58x^4+8x^3+58x^2+159x+6$
• $y^2=159x^6+113x^5+66x^4+75x^3+52x^2+161x+120$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 19599 692687457 18736672536144 498294237640546809 13239644246156138621199 351763980220145356187740416 9346015032604418486017794062247 248314266320589401909428295115928425 6597461725085037794998215278150226367056 175287960541226709478840094655054316090446177

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 116 26068 4326428 705887428 115063688996 18755374494598 3057125336771804 498311415684461956 81224760549897535844 13239635967174192988468

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.az $\times$ 1.163.ax 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 $\F_{163}$.

## 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.ac_ajp $2$ (not in LMFDB) 2.163.c_ajp $2$ (not in LMFDB) 2.163.bw_bir $2$ (not in LMFDB) 2.163.ap_fm $3$ (not in LMFDB) 2.163.ag_acn $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ac_ajp $2$ (not in LMFDB) 2.163.c_ajp $2$ (not in LMFDB) 2.163.bw_bir $2$ (not in LMFDB) 2.163.ap_fm $3$ (not in LMFDB) 2.163.ag_acn $3$ (not in LMFDB) 2.163.abo_bbp $6$ (not in LMFDB) 2.163.abf_tq $6$ (not in LMFDB) 2.163.g_acn $6$ (not in LMFDB) 2.163.p_fm $6$ (not in LMFDB) 2.163.bf_tq $6$ (not in LMFDB) 2.163.bo_bbp $6$ (not in LMFDB)