# Properties

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

# Learn more about

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 49 x + 961 x^{2} - 8869 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0989332971490$, $\pm0.164773451880$ Angle rank: $2$ (numerical) Number field: $$\Q(\zeta_{5})$$ Galois group: $C_4$ Jacobians: 11

This isogeny class is simple and geometrically 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 11 curves, and hence is principally polarizable:

• $y^2=8x^5+180$
• $y^2=171x^6+104x^5+51x^4+45x^3+23x^2+2x+16$
• $y^2=121x^6+92x^5+64x^4+124x^3+52x^2+53x+48$
• $y^2=106x^6+155x^5+91x^4+9x^3+163x^2+103x+86$
• $y^2=57x^6+130x^5+108x^4+127x^3+39x^2+56x+17$
• $y^2=142x^5+37x^4+145x^3+163x^2+20x+111$
• $y^2=59x^6+75x^5+126x^4+38x^3+143x^2+23x+151$
• $y^2=105x^6+59x^5+32x^4+60x^3+116x^2+107x+107$
• $y^2=92x^6+55x^5+164x^4+91x^3+69x^2+33x+130$
• $y^2=28x^6+3x^5+56x^4+128x^3+17x^2+116x+178$
• $y^2=28x^5+53x^4+60x^3+80x^2+173x+83$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24805 1057710005 35144116439905 1151947736663190005 37738739669628951250000 1236354708899487717310069805 40504200483258329534645066940505 1326958066935169846123396699547318405 43472473128820704835415493247002974114005 1424201691985145834249119422445933878720000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 133 32283 5926753 1073293443 194264980098 35161843616283 6364291159308733 1151936660686152003 208500535094782804993 37738596847170094900198

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\zeta_{5})$$.
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.bx_bkz $2$ (not in LMFDB) 2.181.ae_bu $5$ (not in LMFDB) 2.181.l_ach $5$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.bx_bkz $2$ (not in LMFDB) 2.181.ae_bu $5$ (not in LMFDB) 2.181.l_ach $5$ (not in LMFDB) 2.181.l_nx $5$ (not in LMFDB) 2.181.bf_th $5$ (not in LMFDB) 2.181.abf_th $10$ (not in LMFDB) 2.181.al_ach $10$ (not in LMFDB) 2.181.al_nx $10$ (not in LMFDB) 2.181.e_bu $10$ (not in LMFDB)