Invariants
| Base field: | $\F_{211}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 54 x + 1149 x^{2} - 11394 x^{3} + 44521 x^{4}$ |
| Frobenius angles: | $\pm0.0668043685202$, $\pm0.157073280816$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.443968.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $34223$ | $1954783537$ | $88194219385412$ | $3928748835102242473$ | $174914145634352432797223$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $158$ | $43904$ | $9388424$ | $1982094900$ | $418227568118$ | $88245952354910$ | $18619893494488850$ | $3928797481562713828$ | $828976267973758272680$ | $174913992535644989936624$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=80x^6+108x^5+193x^4+34x^3+29x^2+162x+35$
- $y^2=202x^6+170x^5+117x^4+191x^3+164x+118$
- $y^2=64x^6+147x^5+175x^4+196x^3+45x^2+24x+74$
- $y^2=158x^6+196x^5+207x^4+140x^3+24x^2+154x+81$
- $y^2=126x^6+115x^5+110x^4+122x^3+125x^2+16x+8$
- $y^2=119x^6+196x^5+157x^4+123x^3+9x^2+189x+108$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{211}$.
Endomorphism algebra over $\F_{211}$| The endomorphism algebra of this simple isogeny class is 4.0.443968.1. |
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 |
|---|---|---|
| 2.211.cc_bsf | $2$ | (not in LMFDB) |