Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 10 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$ |
| $1 - 19 x + 176 x^{2} - 817 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.223975234504$, $\pm0.259258415261$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 6 |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1190$ | $3405780$ | $6379052120$ | $11712749882400$ | $21616926803537450$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $25$ | $1841$ | $80230$ | $3425977$ | $147045475$ | $6321410354$ | $271817519425$ | $11688188197873$ | $502592544735250$ | $21611482183116161$ |
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 $\F_{43}$.
Endomorphism algebra over $\F_{43}$| The isogeny class factors as 1.43.ak $\times$ 1.43.aj 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 |
|---|---|---|
| 2.43.ab_ae | $2$ | (not in LMFDB) |
| 2.43.b_ae | $2$ | (not in LMFDB) |
| 2.43.t_gu | $2$ | (not in LMFDB) |