# Properties

 Label 2.181.abv_biy 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: $( 1 - 26 x + 181 x^{2} )( 1 - 21 x + 181 x^{2} )$ Frobenius angles: $\pm0.0828936782352$, $\pm0.214985517670$ Angle rank: $2$ (numerical) Jacobians: 30

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 30 curves, and hence is principally polarizable:

• $y^2=19x^6+141x^5+105x^4+63x^3+27x^2+48x+40$
• $y^2=88x^6+131x^5+48x^4+137x^3+90x^2+138x+88$
• $y^2=127x^6+51x^5+7x^4+27x^3+21x^2+57x+133$
• $y^2=159x^6+70x^5+42x^4+108x^3+163x^2+154x+91$
• $y^2=144x^6+95x^5+61x^4+55x^3+154x^2+9x+72$
• $y^2=86x^6+177x^5+117x^4+2x^3+80x^2+110x+78$
• $y^2=11x^6+55x^5+119x^4+116x^3+68x^2+125x+64$
• $y^2=17x^6+61x^5+70x^4+47x^3+131x^2+69x+85$
• $y^2=89x^6+161x^5+108x^4+83x^3+126x^2+33x+95$
• $y^2=78x^6+38x^5+88x^4+95x^3+94x^2+152x+120$
• $y^2=22x^6+88x^5+92x^4+132x^3+84x^2+86x+114$
• $y^2=16x^6+111x^5+64x^4+141x^3+93x^2+5x+174$
• $y^2=78x^6+153x^5+22x^4+51x^3+107x^2+74x+144$
• $y^2=146x^6+164x^5+22x^4+163x^3+17x^2+141x+63$
• $y^2=84x^6+2x^5+15x^4+69x^3+174x^2+10x+93$
• $y^2=98x^6+x^5+48x^4+140x^3+86x^2+133x+158$
• $y^2=87x^6+3x^5+46x^4+16x^3+136x^2+111x+20$
• $y^2=4x^6+87x^5+98x^4+66x^3+47x^2+27x+159$
• $y^2=37x^6+7x^5+129x^4+97x^3+111x^2+148x+103$
• $y^2=4x^6+132x^5+98x^4+122x^3+109x^2+12x+137$
• $y^2=21x^6+34x^5+42x^4+112x^3+123x^2+75x+43$
• $y^2=23x^6+157x^5+115x^4+67x^3+120x^2+162x+110$
• $y^2=13x^6+61x^5+111x^4+67x^3+17x^2+107x+172$
• $y^2=155x^6+20x^5+20x^4+164x^3+124x^2+92x+166$
• $y^2=149x^6+91x^5+91x^4+146x^3+27x^2+46x+150$
• $y^2=22x^6+147x^5+80x^4+120x^3+35x^2+54x+115$
• $y^2=54x^6+17x^5+149x^4+178x^3+54x^2+166x+23$
• $y^2=158x^6+136x^5+166x^4+40x^3+86x^2+32x+174$
• $y^2=33x^6+81x^5+129x^3+117x^2+150x+24$
• $y^2=103x^6+13x^5+79x^4+104x^3+170x^2+98x+130$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25116 1060497984 35154029239056 1151964785540185344 37738717907375914450476 1236354423520245860113920000 40504199243755138075879429472556 1326958063274723719950672862422979584 43472473121139404984130738220523030069136 1424201691976583259286168053461123475852254784

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32369 5928426 1073309329 194264868075 35161835500118 6364290964549695 1151936657508506689 208500535057942132866 37738596846943203185129

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.aba $\times$ 1.181.av 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.af_ahc $2$ (not in LMFDB) 2.181.f_ahc $2$ (not in LMFDB) 2.181.bv_biy $2$ (not in LMFDB) 2.181.ao_ih $3$ (not in LMFDB) 2.181.ac_abl $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.af_ahc $2$ (not in LMFDB) 2.181.f_ahc $2$ (not in LMFDB) 2.181.bv_biy $2$ (not in LMFDB) 2.181.ao_ih $3$ (not in LMFDB) 2.181.ac_abl $3$ (not in LMFDB) 2.181.abo_bdh $6$ (not in LMFDB) 2.181.abc_tp $6$ (not in LMFDB) 2.181.c_abl $6$ (not in LMFDB) 2.181.o_ih $6$ (not in LMFDB) 2.181.bc_tp $6$ (not in LMFDB) 2.181.bo_bdh $6$ (not in LMFDB)