# Properties

 Label 2.181.abw_bkb 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: $( 1 - 25 x + 181 x^{2} )( 1 - 23 x + 181 x^{2} )$ Frobenius angles: $\pm0.120568372405$, $\pm0.173686936480$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=80x^6+120x^5+49x^4+49x^2+120x+80$
• $y^2=21x^6+99x^5+62x^4+87x^3+62x^2+99x+21$
• $y^2=161x^6+39x^5+169x^4+145x^3+169x^2+39x+161$
• $y^2=175x^6+146x^5+82x^4+164x^3+82x^2+146x+175$
• $y^2=78x^6+35x^5+129x^4+146x^3+129x^2+35x+78$
• $y^2=113x^6+121x^5+88x^4+101x^3+88x^2+121x+113$
• $y^2=124x^6+132x^5+35x^4+18x^3+35x^2+132x+124$
• $y^2=40x^6+5x^5+142x^4+137x^3+142x^2+5x+40$
• $y^2=147x^6+85x^5+141x^4+120x^3+141x^2+85x+147$
• $y^2=74x^6+33x^5+54x^4+8x^3+54x^2+33x+74$
• $y^2=30x^6+33x^5+99x^4+128x^3+99x^2+33x+30$
• $y^2=112x^6+121x^5+136x^4+116x^3+136x^2+121x+112$
• $y^2=179x^6+17x^5+170x^4+76x^3+170x^2+17x+179$
• $y^2=14x^6+128x^5+90x^4+116x^3+90x^2+128x+14$
• $y^2=91x^6+19x^5+127x^4+39x^3+127x^2+19x+91$
• $y^2=120x^6+71x^5+56x^4+158x^3+56x^2+71x+120$
• $y^2=136x^6+64x^4+99x^3+64x^2+136$
• $y^2=160x^6+118x^5+79x^4+69x^3+79x^2+118x+160$
• $y^2=88x^6+178x^5+76x^4+137x^3+76x^2+178x+88$
• $y^2=91x^6+116x^5+92x^4+99x^3+92x^2+116x+91$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24963 1059304905 35151592932288 1151973136433003625 37738808042332543339083 1236354853892113884119224320 40504200692811020206567878486723 1326958066936250160702153767055023625 43472473127450616465193874570817350735808 1424201691978829918110375091713342266144717625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 134 32332 5928014 1073317108 194265332054 35161847739862 6364291192235054 1151936660687089828 208500535088211654614 37738596847002735309052

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.az $\times$ 1.181.ax 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.ac_aif $2$ (not in LMFDB) 2.181.c_aif $2$ (not in LMFDB) 2.181.bw_bkb $2$ (not in LMFDB)