Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 51 x + 1069 x^{2} - 10761 x^{3} + 44521 x^{4}$ |
Frobenius angles: | $\pm0.111010858071$, $\pm0.196356372639$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.522717.1 |
Galois group: | $D_{4}$ |
Jacobians: | $30$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34779$ | $1961639937$ | $88233017778909$ | $3928904501846119533$ | $174914625684001415665584$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $161$ | $44059$ | $9392555$ | $1982173435$ | $418228715936$ | $88245964917655$ | $18619893576024209$ | $3928797481236778723$ | $828976267955047275839$ | $174913992535363905379174$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=171x^6+160x^5+21x^4+19x^3+39x^2+142x+62$
- $y^2=21x^6+169x^5+38x^4+4x^3+116x^2+58x+180$
- $y^2=72x^6+9x^5+103x^4+107x^3+95x^2+145x+42$
- $y^2=59x^6+183x^5+159x^4+184x^3+138x^2+51x+1$
- $y^2=177x^6+184x^5+159x^4+93x^3+200x^2+127x+38$
- $y^2=72x^6+24x^5+123x^4+162x^3+121x^2+95x+53$
- $y^2=57x^6+143x^5+165x^4+27x^3+138x^2+x+210$
- $y^2=16x^6+73x^5+37x^4+154x^3+37x^2+98x+116$
- $y^2=152x^6+125x^5+113x^4+117x^3+182x^2+69x+27$
- $y^2=143x^6+170x^5+132x^4+158x^3+144x^2+183x+46$
- $y^2=80x^6+179x^5+88x^4+38x^3+98x^2+139x+34$
- $y^2=166x^6+139x^5+76x^4+67x^3+90x^2+122x+65$
- $y^2=182x^6+30x^5+81x^4+206x^3+134x^2+130x+56$
- $y^2=8x^6+2x^5+169x^4+143x^3+120x^2+110x+82$
- $y^2=22x^6+53x^5+99x^4+205x^3+125x^2+207x+198$
- $y^2=190x^6+155x^5+4x^4+43x^3+60x^2+27x+97$
- $y^2=178x^6+144x^5+163x^4+131x^3+61x^2+77x+146$
- $y^2=90x^6+27x^5+209x^4+37x^3+168x^2+31x+67$
- $y^2=63x^6+104x^5+132x^4+86x^3+36x^2+38x+54$
- $y^2=33x^6+32x^5+145x^4+57x^3+177x^2+91x+97$
- $y^2=47x^6+82x^5+51x^4+98x^3+178x^2+134x+34$
- $y^2=32x^6+143x^5+75x^4+118x^3+190x^2+5x+41$
- $y^2=121x^6+9x^5+122x^4+173x^3+80x^2+36x+191$
- $y^2=170x^6+109x^5+73x^4+44x^3+65x^2+159x+36$
- $y^2=118x^6+110x^5+70x^4+106x^3+78x^2+125x+161$
- $y^2=18x^6+103x^5+43x^4+153x^3+142x^2+100x+50$
- $y^2=85x^6+83x^5+151x^4+92x^3+12x^2+89x+115$
- $y^2=162x^6+33x^5+169x^4+210x^3+66x^2+183x+206$
- $y^2=174x^6+117x^5+60x^4+185x^3+23x^2+35x+146$
- $y^2=124x^6+61x^5+127x^4+41x^3+24x^2+101x+85$
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 4.0.522717.1. |
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_bpd | $2$ | (not in LMFDB) |