Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 53 x + 1120 x^{2} - 11183 x^{3} + 44521 x^{4}$ |
Frobenius angles: | $\pm0.0585525127533$, $\pm0.181846139883$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2013752.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34406$ | $1956944468$ | $88205127830024$ | $3928782269701491872$ | $174914183806045452700506$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $159$ | $43953$ | $9389586$ | $1982111769$ | $418227659389$ | $88245949196514$ | $18619893364855095$ | $3928797478558913265$ | $828976267921233207270$ | $174913992534925959951793$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=58x^6+99x^5+85x^4+209x^3+116x^2+195x+84$
- $y^2=72x^6+190x^5+75x^4+208x^3+13x^2+64x+176$
- $y^2=142x^6+39x^5+129x^4+100x^3+100x^2+137x+186$
- $y^2=46x^6+127x^5+81x^4+153x^3+155x^2+195x+101$
- $y^2=141x^6+107x^5+22x^4+173x^3+118x^2+145x+66$
- $y^2=198x^6+125x^5+39x^4+198x^3+105x^2+166x+138$
- $y^2=31x^6+164x^5+182x^4+62x^3+35x^2+133x+29$
- $y^2=43x^6+58x^5+31x^4+83x^3+93x^2+60x+114$
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 4.0.2013752.2. |
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.cb_brc | $2$ | (not in LMFDB) |