Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 913 x^{2} - 8507 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.132251908937$, $\pm0.187299602773$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.657725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $13$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $25121$ | $1060834709$ | $35158215653501$ | $1151992660939088309$ | $37738847788163620114176$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $135$ | $32379$ | $5929131$ | $1073335299$ | $194265536650$ | $35161848751323$ | $6364291171661775$ | $1151936659945323459$ | $208500535074017267211$ | $37738596846803275495654$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=153x^6+28x^5+123x^4+122x^3+166x^2+136x+123$
- $y^2=17x^6+180x^5+42x^4+162x^3+41x^2+157x+18$
- $y^2=83x^6+171x^5+11x^4+103x^3+154x^2+96x+22$
- $y^2=113x^6+172x^5+120x^4+115x^3+8x^2+122x+74$
- $y^2=107x^6+62x^5+171x^4+162x^3+15x^2+84x+40$
- $y^2=134x^6+148x^5+100x^4+164x^3+152x^2+38x+137$
- $y^2=162x^6+78x^5+148x^4+4x^3+133x^2+80x+29$
- $y^2=36x^6+82x^5+91x^4+87x^3+79x^2+42x+93$
- $y^2=149x^5+25x^3+135x^2+111x+54$
- $y^2=40x^6+75x^5+2x^4+78x^3+161x^2+154x+22$
- $y^2=167x^6+23x^5+86x^4+42x^3+125x^2+177x+98$
- $y^2=42x^6+129x^5+137x^4+13x^3+173x^2+9x+88$
- $y^2=92x^6+55x^5+104x^4+25x^3+35x^2+175x+49$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The endomorphism algebra of this simple isogeny class is 4.0.657725.1. |
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.bv_bjd | $2$ | (not in LMFDB) |