Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 51 x + 1064 x^{2} - 10761 x^{3} + 44521 x^{4}$ |
Frobenius angles: | $\pm0.0689749294301$, $\pm0.215789007231$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.14104728.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34774$ | $1961184052$ | $88225823259544$ | $3928843667018672928$ | $174914263613210071753834$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $161$ | $44049$ | $9391790$ | $1982142745$ | $418227850211$ | $88245945902850$ | $18619893238773449$ | $3928797476445449713$ | $828976267905016489274$ | $174913992535141945167249$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=156x^6+140x^5+18x^4+66x^3+194x^2+166x+127$
- $y^2=77x^6+17x^5+101x^4+64x^3+175x^2+127x+9$
- $y^2=74x^6+208x^5+69x^4+33x^3+189x^2+181x+195$
- $y^2=205x^6+180x^5+119x^4+161x^3+175x^2+181x+191$
- $y^2=34x^6+44x^5+34x^4+5x^3+92x^2+123x+76$
- $y^2=60x^6+87x^5+87x^4+114x^3+126x^2+28x+190$
- $y^2=138x^6+83x^5+11x^4+7x^3+83x^2+47x+91$
- $y^2=198x^6+75x^5+94x^4+147x^3+166x^2+94$
- $y^2=41x^6+199x^5+134x^4+109x^3+210x^2+166x+109$
- $y^2=94x^6+21x^5+203x^4+87x^3+144x^2+8x+72$
- $y^2=134x^6+186x^5+125x^4+56x^3+16x^2+102x+39$
- $y^2=88x^6+184x^5+49x^4+8x^3+181x^2+188x+194$
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 4.0.14104728.1. |
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_boy | $2$ | (not in LMFDB) |