Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 51 x + 1061 x^{2} - 10761 x^{3} + 44521 x^{4}$ |
Frobenius angles: | $\pm0.0371443861218$, $\pm0.224073418146$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.101125.1 |
Galois group: | $D_{4}$ |
Jacobians: | $18$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34771$ | $1960910545$ | $88221506624581$ | $3928807071086738445$ | $174914043811274806216816$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $161$ | $44043$ | $9391331$ | $1982124283$ | $418227324656$ | $88245934085463$ | $18619893017410601$ | $3928797472879451683$ | $828976267854176686751$ | $174913992534470841319398$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=20x^6+131x^5+194x^4+21x^3+55x^2+78x+202$
- $y^2=32x^6+16x^5+101x^4+168x^3+39x^2+46x+147$
- $y^2=142x^6+185x^5+154x^4+150x^3+7x^2+73x+167$
- $y^2=108x^6+13x^5+155x^4+101x^3+4x^2+128x+42$
- $y^2=13x^6+171x^5+x^4+62x^3+150x^2+175x+141$
- $y^2=165x^6+50x^5+17x^4+19x^3+203x^2+208x+111$
- $y^2=62x^6+207x^5+198x^4+167x^3+126x^2+40x+153$
- $y^2=152x^6+91x^5+105x^4+49x^3+210x^2+107x+172$
- $y^2=100x^6+168x^5+122x^4+209x^3+39x^2+171x+166$
- $y^2=71x^6+24x^5+146x^4+34x^3+72x^2+197x+41$
- $y^2=117x^6+119x^5+100x^4+174x^3+99x^2+148x+23$
- $y^2=3x^6+53x^5+102x^4+113x^3+102x^2+82x+160$
- $y^2=143x^6+143x^5+159x^4+135x^3+113x^2+172x+143$
- $y^2=152x^6+138x^5+71x^4+154x^3+125x^2+137x+122$
- $y^2=152x^6+175x^5+28x^4+77x^3+203x^2+145x+116$
- $y^2=153x^6+194x^5+82x^4+88x^3+116x^2+93x+102$
- $y^2=41x^6+189x^5+170x^4+2x^3+123x^2+41x+117$
- $y^2=108x^6+206x^5+101x^4+67x^3+92x^2+25x+146$
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 4.0.101125.1. |
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.bz_bov | $2$ | (not in LMFDB) |