# Properties

 Label 2.181.abu_bhs 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: $1 - 46 x + 876 x^{2} - 8326 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0160657258716$, $\pm0.248310478721$ Angle rank: $2$ (numerical) Number field: 4.0.2376000.1 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=60x^6+57x^5+16x^4+41x^3+63x^2+90x+25$
• $y^2=131x^6+60x^5+6x^4+176x^3+58x^2+144x+38$
• $y^2=10x^6+18x^5+84x^4+28x^3+32x^2+124x+124$
• $y^2=67x^6+10x^5+147x^4+57x^3+156x^2+135x+68$
• $y^2=x^6+130x^5+168x^4+174x^3+117x^2+66x+61$
• $y^2=16x^6+126x^5+23x^4+153x^3+157x^2+79x+19$
• $y^2=129x^6+64x^5+110x^3+2x^2+129x+44$
• $y^2=69x^6+54x^5+67x^4+49x^3+92x^2+177x+143$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25266 1061424660 35153368060626 1151938068205665360 37738555284740103399666 1236353786555283316251291060 40504197362480181857744905499346 1326958058893234075220347881986012160 43472473112963795676652186169674459878306 1424201691963442899882804236471069814325912500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32398 5928316 1073284438 194264030956 35161817384878 6364290668951176 1151936653704921118 208500535018730678056 37738596846595009015198

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.2376000.1.
All geometric endomorphisms are defined over $\F_{181}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.bu_bhs $2$ (not in LMFDB)