# Properties

 Label 2.181.abu_bhy 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: $( 1 - 26 x + 181 x^{2} )( 1 - 20 x + 181 x^{2} )$ Frobenius angles: $\pm0.0828936782352$, $\pm0.233262291643$ Angle rank: $2$ (numerical) Jacobians: 100

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 100 curves, and hence is principally polarizable:

• $y^2=126x^6+173x^5+155x^4+12x^3+171x^2+77x+87$
• $y^2=125x^6+97x^5+132x^4+50x^3+132x^2+97x+125$
• $y^2=113x^6+55x^5+83x^4+98x^3+131x^2+151x+24$
• $y^2=22x^6+47x^5+9x^4+12x^3+172x^2+15x+139$
• $y^2=2x^6+30x^5+38x^4+74x^3+141x^2+113x+140$
• $y^2=49x^6+150x^5+153x^4+155x^3+153x^2+150x+49$
• $y^2=19x^6+84x^5+36x^4+151x^3+63x^2+18x+119$
• $y^2=94x^6+129x^5+27x^4+143x^3+53x^2+111x+83$
• $y^2=161x^6+144x^5+75x^4+82x^3+150x^2+63x+95$
• $y^2=154x^6+71x^5+104x^4+94x^3+104x^2+71x+154$
• $y^2=47x^6+115x^5+119x^4+83x^3+139x^2+164x+76$
• $y^2=96x^6+23x^5+116x^4+128x^3+116x^2+23x+96$
• $y^2=175x^6+99x^5+174x^4+151x^3+179x^2+178x+174$
• $y^2=94x^6+32x^5+54x^4+89x^3+109x^2+35x+2$
• $y^2=67x^6+113x^5+56x^4+57x^3+142x^2+103x+154$
• $y^2=157x^6+9x^5+76x^4+66x^3+171x^2+177x+26$
• $y^2=71x^6+146x^5+52x^4+40x^3+76x^2+53x+123$
• $y^2=114x^6+3x^5+9x^4+20x^3+81x^2+62x+27$
• $y^2=25x^6+11x^5+166x^4+159x^3+134x^2+79x+66$
• $y^2=85x^6+14x^5+115x^4+x^3+29x^2+75x+34$
• and 80 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25272 1061828352 35158284310968 1151969933920665600 37738699782737963730552 1236354297238790133385363200 40504198847814019653163452212472 1326958062593061604562509210936934400 43472473121304776474215552299413346837048 1424201691982291105658430207832510831646752512

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32410 5929144 1073314126 194264774776 35161831908682 6364290902336776 1151936656916753566 208500535058735279464 37738596847094450100730

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.aba $\times$ 1.181.au 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.ag_agc $2$ (not in LMFDB) 2.181.g_agc $2$ (not in LMFDB) 2.181.bu_bhy $2$ (not in LMFDB) 2.181.an_io $3$ (not in LMFDB) 2.181.ab_as $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.ag_agc $2$ (not in LMFDB) 2.181.g_agc $2$ (not in LMFDB) 2.181.bu_bhy $2$ (not in LMFDB) 2.181.an_io $3$ (not in LMFDB) 2.181.ab_as $3$ (not in LMFDB) 2.181.abs_bfy $4$ (not in LMFDB) 2.181.ai_aec $4$ (not in LMFDB) 2.181.i_aec $4$ (not in LMFDB) 2.181.bs_bfy $4$ (not in LMFDB) 2.181.abn_bco $6$ (not in LMFDB) 2.181.abb_ti $6$ (not in LMFDB) 2.181.b_as $6$ (not in LMFDB) 2.181.n_io $6$ (not in LMFDB) 2.181.bb_ti $6$ (not in LMFDB) 2.181.bn_bco $6$ (not in LMFDB) 2.181.abl_bbc $12$ (not in LMFDB) 2.181.az_su $12$ (not in LMFDB) 2.181.al_jc $12$ (not in LMFDB) 2.181.ab_u $12$ (not in LMFDB) 2.181.b_u $12$ (not in LMFDB) 2.181.l_jc $12$ (not in LMFDB) 2.181.z_su $12$ (not in LMFDB) 2.181.bl_bbc $12$ (not in LMFDB)