Properties

 Label 2.181.aby_bly 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: $( 1 - 26 x + 181 x^{2} )( 1 - 24 x + 181 x^{2} )$ Frobenius angles: $\pm0.0828936782352$, $\pm0.149335043618$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=19x^6+94x^5+110x^4+130x^3+77x^2+180x+141$
• $y^2=57x^6+49x^5+180x^4+138x^3+180x^2+49x+57$
• $y^2=62x^6+20x^5+68x^4+26x^3+53x^2+136x+39$
• $y^2=90x^6+4x^5+179x^4+70x^3+88x^2+142x+57$
• $y^2=96x^6+77x^5+109x^4+22x^3+109x^2+77x+96$
• $y^2=35x^6+96x^5+34x^4+22x^3+73x^2+58x+22$
• $y^2=66x^6+175x^5+107x^4+73x^3+107x^2+175x+66$
• $y^2=81x^6+140x^5+54x^4+x^3+54x^2+140x+81$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 24648 1056117504 35136641521800 1151922333134536704 37738671201839627609928 1236354562792731291567840000 40504200264537239477794303173768 1326958066874666182738394385306353664 43472473129869101358024477738575424112200 1424201691989956968566809907815194727332797184

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 132 32234 5925492 1073269774 194264627652 35161839461018 6364291124941812 1151936660633628574 208500535099811072772 37738596847297580676554

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The isogeny class factors as 1.181.aba $\times$ 1.181.ay 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.ac_akc $2$ (not in LMFDB) 2.181.c_akc $2$ (not in LMFDB) 2.181.by_bly $2$ (not in LMFDB) 2.181.ar_hm $3$ (not in LMFDB) 2.181.af_adq $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.181.ac_akc $2$ (not in LMFDB) 2.181.c_akc $2$ (not in LMFDB) 2.181.by_bly $2$ (not in LMFDB) 2.181.ar_hm $3$ (not in LMFDB) 2.181.af_adq $3$ (not in LMFDB) 2.181.abr_bfm $6$ (not in LMFDB) 2.181.abf_uk $6$ (not in LMFDB) 2.181.f_adq $6$ (not in LMFDB) 2.181.r_hm $6$ (not in LMFDB) 2.181.bf_uk $6$ (not in LMFDB) 2.181.br_bfm $6$ (not in LMFDB)