# Properties

 Label 2.181.abx_bky Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $( 1 - 26 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$ Frobenius angles: $\pm0.0828936782352$, $\pm0.173686936480$ Angle rank: $2$ (numerical) Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=93x^6+112x^5+161x^4+22x^3+65x^2+32x+72$
• $y^2=15x^6+65x^5+40x^4+47x^3+176x^2+43x+10$
• $y^2=146x^6+148x^5+86x^4+41x^3+23x^2+157x+51$
• $y^2=156x^6+98x^5+71x^4+140x^3+32x^2+26x+127$
• $y^2=46x^6+4x^5+77x^4+75x^3+164x^2+75x+51$
• $y^2=54x^6+155x^5+138x^4+151x^3+124x^2+56x+63$
• $y^2=158x^6+54x^5+95x^4+65x^3+64x^2+x+124$
• $y^2=80x^6+161x^5+57x^4+149x^3+145x^2+31x+106$
• $y^2=91x^6+39x^5+101x^4+6x^3+117x^2+32x+28$
• $y^2=32x^6+137x^5+134x^4+72x^3+45x^2+22$
• $y^2=168x^6+149x^5+157x^4+112x^3+24x^2+121x+10$
• $y^2=134x^6+120x^5+74x^4+66x^3+108x^2+117x+114$
• $y^2=135x^6+139x^5+27x^4+38x^3+69x^2+127x+6$
• $y^2=40x^6+174x^5+147x^4+6x^3+102x^2+151x+140$
• $y^2=49x^6+157x^5+87x^4+121x^3+176x^2+16x+137$
• $y^2=158x^6+64x^5+34x^4+39x^3+114x^2+12x+128$
• $y^2=152x^6+117x^5+165x^4+62x^3+138x^2+142x+105$
• $y^2=164x^6+151x^5+112x^4+76x^3+x^2+121x+12$
• $y^2=101x^6+71x^5+96x^4+104x^3+86x^2+138x+58$
• $y^2=146x^6+114x^5+170x^4+66x^3+115x^2+76x+48$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24804 1057642560 35143243402176 1151941551823146240 37738708209327963498804 1236354581202761315602944000 40504200050248004980084185238644 1326958065691480231979711021662786560 43472473125847748392377503408285560545216 1424201691979719109153346875283106135780264000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 133 32281 5926606 1073287681 194264818153 35161839984598 6364291091271253 1151936659606500961 208500535080524057686 37738596847026297156001

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.aba $\times$ 1.181.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 $\F_{181}$.

## 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 2.181.ad_ajc $2$ (not in LMFDB) 2.181.d_ajc $2$ (not in LMFDB) 2.181.bx_bky $2$ (not in LMFDB) 2.181.aq_ht $3$ (not in LMFDB) 2.181.ae_acx $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.ad_ajc $2$ (not in LMFDB) 2.181.d_ajc $2$ (not in LMFDB) 2.181.bx_bky $2$ (not in LMFDB) 2.181.aq_ht $3$ (not in LMFDB) 2.181.ae_acx $3$ (not in LMFDB) 2.181.abq_bet $6$ (not in LMFDB) 2.181.abe_ud $6$ (not in LMFDB) 2.181.e_acx $6$ (not in LMFDB) 2.181.q_ht $6$ (not in LMFDB) 2.181.be_ud $6$ (not in LMFDB) 2.181.bq_bet $6$ (not in LMFDB)