Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 12 x + 43 x^{2} )( 1 - 11 x + 43 x^{2} )$ |
| $1 - 23 x + 218 x^{2} - 989 x^{3} + 1849 x^{4}$ | |
| Frobenius angles: | $\pm0.132197172840$, $\pm0.183291501244$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1056$ | $3252480$ | $6314191488$ | $11697804518400$ | $21616652728377696$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $21$ | $1757$ | $79416$ | $3421609$ | $147043611$ | $6321640934$ | $271820282265$ | $11688207725521$ | $502592628730248$ | $21611482214852957$ |
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.am $\times$ 1.43.al 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_abu | $2$ | (not in LMFDB) |
| 2.43.b_abu | $2$ | (not in LMFDB) |
| 2.43.x_ik | $2$ | (not in LMFDB) |