# Properties

 Label 2.181.abu_bid 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: $( 1 - 25 x + 181 x^{2} )( 1 - 21 x + 181 x^{2} )$ Frobenius angles: $\pm0.120568372405$, $\pm0.214985517670$ Angle rank: $2$ (numerical) Jacobians: 54

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 54 curves, and hence is principally polarizable:

• $y^2=171x^6+169x^5+65x^4+111x^3+37x^2+62x+164$
• $y^2=154x^6+12x^5+111x^4+35x^3+13x^2+64x+80$
• $y^2=165x^6+173x^5+112x^4+95x^3+116x^2+29x+143$
• $y^2=174x^6+50x^5+67x^4+38x^3+9x^2+159x+19$
• $y^2=180x^6+14x^5+84x^4+64x^3+59x^2+158x+53$
• $y^2=109x^6+55x^5+30x^4+113x^3+58x^2+78x+26$
• $y^2=50x^6+178x^5+9x^4+166x^3+98x^2+128x+110$
• $y^2=63x^6+67x^5+11x^4+127x^3+106x^2+99x+92$
• $y^2=137x^6+95x^5+104x^4+6x^3+23x^2+24x+62$
• $y^2=92x^6+7x^5+27x^4+63x^3+30x^2+157x+116$
• $y^2=44x^6+117x^5+97x^4+61x^3+63x^2+145x+38$
• $y^2=36x^6+7x^5+18x^3+22x+117$
• $y^2=127x^6+81x^5+6x^4+147x^3+105x^2+19x+73$
• $y^2=174x^6+16x^5+129x^4+146x^3+152x^2+101x+64$
• $y^2=58x^6+2x^5+171x^4+27x^3+86x^2+175x+3$
• $y^2=43x^6+171x^5+66x^4+146x^3+157x^2+63x+138$
• $y^2=52x^6+88x^5+146x^4+147x^3+155x^2+23x+169$
• $y^2=110x^6+75x^5+57x^4+63x^3+153x^2+43x+175$
• $y^2=35x^6+5x^5+132x^4+134x^3+99x^2+82x+159$
• $y^2=60x^6+103x^5+9x^4+165x^3+134x^2+57x+175$
• and 34 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25277 1062164817 35162381331728 1151996370787078425 37738817740406149256477 1236354696209563650303897600 40504199886318140508072958398677 1326958064519493646406046354462246825 43472473122742273056773508647180261306768 1424201691975694068243198227738783676944777937

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 136 32420 5929834 1073338756 194265381976 35161843255382 6364291065513496 1151936658589095556 208500535065629729794 37738596846919641338180

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.az $\times$ 1.181.av 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.ae_agh $2$ (not in LMFDB) 2.181.e_agh $2$ (not in LMFDB) 2.181.bu_bid $2$ (not in LMFDB)