Invariants
| Base field: | $\F_{211}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 26 x + 211 x^{2} )( 1 - 25 x + 211 x^{2} )$ |
| $1 - 51 x + 1072 x^{2} - 10761 x^{3} + 44521 x^{4}$ | |
| Frobenius angles: | $\pm0.147206137144$, $\pm0.170129106792$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $34782$ | $1961913492$ | $88237334567448$ | $3928940907708247200$ | $174914840367017982428802$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $161$ | $44065$ | $9393014$ | $1982191801$ | $418229229251$ | $88245975918562$ | $18619893759456521$ | $3928797483429109681$ | $828976267964803644434$ | $174913992534986905240705$ |
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.aba $\times$ 1.211.az 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_aiu | $2$ | (not in LMFDB) |
| 2.211.b_aiu | $2$ | (not in LMFDB) |
| 2.211.bz_bpg | $2$ | (not in LMFDB) |