# Properties

 Label 2.181.abu_bic 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: $1 - 46 x + 886 x^{2} - 8326 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.112775809299$, $\pm0.219413980321$ Angle rank: $2$ (numerical) Number field: 4.0.638000.2 Galois group: $D_{4}$ Jacobians: 48

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 48 curves, and hence is principally polarizable:

• $y^2=49x^6+128x^5+93x^4+91x^3+5x^2+71x+152$
• $y^2=155x^6+8x^5+98x^4+28x^3+140x^2+78x+114$
• $y^2=153x^6+99x^5+6x^4+56x^3+49x^2+165x+136$
• $y^2=155x^6+111x^5+160x^4+78x^3+60x^2+27x+15$
• $y^2=174x^6+80x^5+84x^4+16x^3+25x^2+37x+21$
• $y^2=133x^6+61x^5+30x^4+66x^3+57x^2+27x+18$
• $y^2=153x^6+119x^5+137x^4+10x^3+20x^2+30x+51$
• $y^2=125x^6+134x^5+168x^4+137x^3+62x^2+79x+53$
• $y^2=90x^6+75x^5+78x^4+26x^3+103x^2+120x+175$
• $y^2=25x^6+10x^5+106x^4+167x^3+6x+124$
• $y^2=17x^6+2x^5+126x^4+70x^3+14x^2+136x+27$
• $y^2=174x^6+176x^5+137x^4+20x^3+91x^2+123x+119$
• $y^2=38x^6+42x^5+165x^4+157x^3+44x^2+116x+180$
• $y^2=84x^6+73x^5+152x^4+107x^3+120x^2+124x+63$
• $y^2=156x^6+114x^5+154x^4+51x^3+54x^2+51x+58$
• $y^2=51x^6+161x^5+124x^4+15x^3+143x^2+156x+177$
• $y^2=119x^6+38x^5+33x^4+120x^3+163x^2+4x+50$
• $y^2=144x^6+138x^5+64x^4+144x^3+87x^2+119x+1$
• $y^2=90x^6+98x^5+128x^4+61x^3+112x^2+147x+99$
• $y^2=89x^6+146x^5+71x^4+129x^3+154x^2+75x+88$
• and 28 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25276 1062097520 35161561916956 1151991091987915520 37738794327587194977916 1236354618347055078294798320 40504199693028004271465112291676 1326958064217100461291533141826744320 43472473122842955767935397528873245771516 1424201691978533439793078199515795901980950000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32418 5929696 1073333838 194265261456 35161841040978 6364291035142456 1151936658326587038 208500535066112619256 37738596846994879205698

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.638000.2.
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_bic $2$ (not in LMFDB)