Invariants
Base field: | $\F_{211}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 28 x + 211 x^{2} )( 1 - 27 x + 211 x^{2} )$ |
$1 - 55 x + 1178 x^{2} - 11605 x^{3} + 44521 x^{4}$ | |
Frobenius angles: | $\pm0.0859092328146$, $\pm0.120343810545$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $34040$ | $1952534400$ | $88181902763360$ | $3928703908696358400$ | $174914043716682909521000$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $157$ | $43853$ | $9387112$ | $1982072233$ | $418227324427$ | $88245952614038$ | $18619893588097777$ | $3928797484527349393$ | $828976268039528082712$ | $174913992536835162567773$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
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.abb 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.ab_amw | $2$ | (not in LMFDB) |
2.211.b_amw | $2$ | (not in LMFDB) |
2.211.cd_bti | $2$ | (not in LMFDB) |