# Properties

 Label 2.163.abs_bev 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: $( 1 - 25 x + 163 x^{2} )( 1 - 19 x + 163 x^{2} )$ Frobenius angles: $\pm0.0652307277549$, $\pm0.232879815243$ Angle rank: $2$ (numerical) Jacobians: 40

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 40 curves, and hence is principally polarizable:

• $y^2=77x^6+48x^5+51x^4+140x^3+120x^2+75x+94$
• $y^2=72x^6+144x^5+124x^4+5x^3+141x^2+113x+111$
• $y^2=5x^6+159x^5+21x^4+43x^3+31x^2+84x+75$
• $y^2=70x^6+125x^5+83x^4+78x^3+139x^2+35x+84$
• $y^2=113x^6+35x^5+121x^4+146x^3+86x^2+48x+160$
• $y^2=72x^6+21x^5+19x^4+150x^2+8x+105$
• $y^2=101x^6+x^5+9x^4+157x^3+9x^2+x+101$
• $y^2=12x^6+10x^5+154x^4+7x^3+89x^2+16x+147$
• $y^2=81x^6+40x^5+126x^4+72x^3+54x^2+14x+4$
• $y^2=133x^6+20x^5+73x^4+136x^3+67x^2+107x+120$
• $y^2=19x^6+79x^5+55x^4+99x^3+64x^2+106x+120$
• $y^2=29x^6+66x^5+46x^4+85x^3+41x^2+19x+124$
• $y^2=31x^6+33x^5+114x^4+32x^3+17x^2+150x+125$
• $y^2=83x^6+10x^5+18x^4+124x^3+17x^2+40x+78$
• $y^2=4x^6+139x^5+115x^4+72x^3+22x^2+45x+94$
• $y^2=46x^6+91x^5+55x^4+104x^3+115x^2+138x+106$
• $y^2=138x^6+153x^5+55x^4+96x^3+58x^2+105x+99$
• $y^2=42x^6+50x^5+110x^4+126x^3+105x^2+64x+148$
• $y^2=67x^6+162x^5+50x^4+42x^3+86x^2+153x+44$
• $y^2=130x^6+106x^5+5x^4+77x^3+108x^2+112x+76$
• and 20 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20155 697100985 18751177806640 498322461366498825 13239663301093020866275 351763885163745822325259520 9346014560125457979843103457035 248314265048570520303390913653335625 6597461722779315532077291816161722454320 175287960539002911616232604806683739363272425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 120 26236 4329780 705927412 115063854600 18755369426374 3057125182221720 498311413131803428 81224760521510597580 13239635967006227806636

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.az $\times$ 1.163.at 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.ag_aft $2$ (not in LMFDB) 2.163.g_aft $2$ (not in LMFDB) 2.163.bs_bev $2$ (not in LMFDB) 2.163.al_gs $3$ (not in LMFDB) 2.163.ac_d $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ag_aft $2$ (not in LMFDB) 2.163.g_aft $2$ (not in LMFDB) 2.163.bs_bev $2$ (not in LMFDB) 2.163.al_gs $3$ (not in LMFDB) 2.163.ac_d $3$ (not in LMFDB) 2.163.abk_yz $6$ (not in LMFDB) 2.163.abb_sk $6$ (not in LMFDB) 2.163.c_d $6$ (not in LMFDB) 2.163.l_gs $6$ (not in LMFDB) 2.163.bb_sk $6$ (not in LMFDB) 2.163.bk_yz $6$ (not in LMFDB)