Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 28 x + 211 x^{2} )( 1 - 23 x + 211 x^{2} )$ |
$1 - 51 x + 1066 x^{2} - 10761 x^{3} + 44521 x^{4}$ | |
Frobenius angles: | $\pm0.0859092328146$, $\pm0.209200140274$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $60$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34776$ | $1961366400$ | $88228701048096$ | $3928868024708390400$ | $174914409081391472847816$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $161$ | $44053$ | $9392096$ | $1982155033$ | $418228198031$ | $88245953610838$ | $18619893378416141$ | $3928797478533788593$ | $828976267930170505376$ | $174913992535362047822773$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 60 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=105x^6+163x^5+27x^4+29x^3+129x^2+40x+39$
- $y^2=186x^6+195x^5+101x^4+72x^3+77x^2+93x+84$
- $y^2=171x^6+158x^5+30x^4+59x^3+208x^2+61x+194$
- $y^2=102x^6+72x^5+113x^4+192x^3+186x^2+80x+189$
- $y^2=123x^6+96x^5+143x^4+196x^3+187x^2+152x+167$
- $y^2=98x^6+147x^5+25x^4+22x^3+161x^2+144x+130$
- $y^2=175x^6+48x^5+177x^4+126x^3+205x^2+104x+76$
- $y^2=41x^6+31x^5+186x^4+94x^3+143x^2+180x+168$
- $y^2=189x^6+29x^5+147x^4+68x^3+121x^2+57x+87$
- $y^2=3x^6+192x^5+46x^4+189x^3+199x^2+85x+165$
- $y^2=134x^6+85x^5+128x^4+61x^3+36x^2+204x+201$
- $y^2=198x^6+151x^5+164x^4+39x^3+18x^2+124x+203$
- $y^2=133x^6+137x^5+56x^4+72x^3+176x^2+196x+81$
- $y^2=15x^6+82x^5+151x^4+30x^3+119x^2+x+59$
- $y^2=70x^6+153x^5+29x^4+139x^3+43x^2+83x+92$
- $y^2=39x^6+174x^5+148x^4+6x^3+57x^2+82x+1$
- $y^2=188x^6+x^5+158x^4+172x^3+79x^2+136x+29$
- $y^2=206x^6+20x^5+23x^4+49x^3+208x^2+86x+26$
- $y^2=74x^6+31x^5+28x^4+185x^3+164x^2+176x+106$
- $y^2=138x^6+169x^5+140x^4+55x^3+140x^2+193x+41$
- and 40 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{211}$.
Endomorphism algebra over $\F_{211}$The isogeny class factors as 1.211.abc $\times$ 1.211.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.af_aio | $2$ | (not in LMFDB) |
2.211.f_aio | $2$ | (not in LMFDB) |
2.211.bz_bpa | $2$ | (not in LMFDB) |