# Properties

 Label 2.181.aca_bny 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: $( 1 - 26 x + 181 x^{2} )^{2}$ Frobenius angles: $\pm0.0828936782352$, $\pm0.0828936782352$ Angle rank: $1$ (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:

• $y^2=x^6+60x^3+67$
• $y^2=51x^6+143x^5+26x^4+66x^3+26x^2+143x+51$
• $y^2=x^6+180$
• $y^2=92x^6+114x^5+69x^4+16x^3+131x^2+48x+118$
• $y^2=40x^6+170x^4+170x^2+40$
• $y^2=107x^6+51x^5+165x^4+150x^3+165x^2+51x+107$
• $y^2=68x^6+131x^5+130x^4+81x^3+130x^2+131x+68$
• $y^2=69x^6+33x^4+33x^2+69$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24336 1052872704 35120842048656 1151865665532002304 37738505921630646287376 1236354164391636545149440000 40504199512701896227619649361296 1326958066062810715140931778289598464 43472473131239557380299012767952375947536 1424201692002246333765865470710586879106781184

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 130 32134 5922826 1073216974 194263776850 35161828130518 6364291006808410 1151936659928854174 208500535106383986466 37738596847623225142054

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.aba 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-3})$$$)$
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.a_amc $2$ (not in LMFDB) 2.181.ca_bny $2$ (not in LMFDB) 2.181.at_gy $3$ (not in LMFDB) 2.181.ah_afc $3$ (not in LMFDB) 2.181.o_pv $3$ (not in LMFDB) 2.181.ba_tb $3$ (not in LMFDB) 2.181.bm_bbv $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.a_amc $2$ (not in LMFDB) 2.181.ca_bny $2$ (not in LMFDB) 2.181.at_gy $3$ (not in LMFDB) 2.181.ah_afc $3$ (not in LMFDB) 2.181.o_pv $3$ (not in LMFDB) 2.181.ba_tb $3$ (not in LMFDB) 2.181.bm_bbv $3$ (not in LMFDB) 2.181.a_mc $4$ (not in LMFDB) 2.181.abt_bgy $6$ (not in LMFDB) 2.181.abm_bbv $6$ (not in LMFDB) 2.181.abh_uy $6$ (not in LMFDB) 2.181.aba_tb $6$ (not in LMFDB) 2.181.ao_pv $6$ (not in LMFDB) 2.181.am_iv $6$ (not in LMFDB) 2.181.a_b $6$ (not in LMFDB) 2.181.a_mb $6$ (not in LMFDB) 2.181.h_afc $6$ (not in LMFDB) 2.181.m_iv $6$ (not in LMFDB) 2.181.t_gy $6$ (not in LMFDB) 2.181.bh_uy $6$ (not in LMFDB) 2.181.bt_bgy $6$ (not in LMFDB) 2.181.a_amb $12$ (not in LMFDB) 2.181.a_ab $12$ (not in LMFDB)