Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 53 x + 1121 x^{2} - 11183 x^{3} + 44521 x^{4}$ |
Frobenius angles: | $\pm0.0724318417965$, $\pm0.176533229289$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.188773.1 |
Galois group: | $D_{4}$ |
Jacobians: | $15$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34407$ | $1957035753$ | $88206623320113$ | $3928795657851881853$ | $174914270143095943440432$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $159$ | $43955$ | $9389745$ | $1982118523$ | $418227865824$ | $88245954263063$ | $18619893469962363$ | $3928797480448301059$ | $828976267950911695233$ | $174913992535330594085990$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=208x^6+83x^5+117x^4+67x^3+48x^2+48x+204$
- $y^2=19x^6+118x^5+26x^4+168x^3+14x^2+17x+28$
- $y^2=18x^6+32x^5+36x^4+158x^3+73x^2+158x+43$
- $y^2=8x^6+55x^5+114x^4+9x^3+85x^2+45x+209$
- $y^2=145x^6+160x^5+5x^4+71x^3+114x^2+172x+74$
- $y^2=128x^6+175x^5+81x^4+32x^3+173x^2+156x+197$
- $y^2=185x^6+143x^5+71x^4+16x^3+18x^2+155x+137$
- $y^2=31x^6+183x^5+74x^4+44x^3+168x^2+30x+78$
- $y^2=98x^6+34x^5+163x^4+180x^3+204x^2+171x+136$
- $y^2=122x^6+135x^5+112x^4+11x^3+170x^2+209x+31$
- $y^2=110x^6+188x^5+79x^4+19x^3+126x^2+91x+12$
- $y^2=119x^6+191x^5+67x^4+13x^3+176x^2+176x+136$
- $y^2=116x^6+100x^5+198x^4+200x^3+116x^2+136x+105$
- $y^2=162x^5+194x^4+197x^3+152x^2+3x+79$
- $y^2=112x^6+42x^5+141x^4+120x^3+63x^2+82x+88$
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 4.0.188773.1. |
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.cb_brd | $2$ | (not in LMFDB) |