Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4} )$ |
| $1 - 23 x + 242 x^{2} - 1482 x^{3} + 5566 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.0783210629050$, $\pm0.186011988595$, $\pm0.297557123995$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4304$ | $136212992$ | $1813789084688$ | $21994887726770176$ | $266778314171123801344$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $485$ | $12253$ | $280865$ | $6439796$ | $148037321$ | $3404798279$ | $78311017649$ | $1801154300359$ | $41426522399660$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The isogeny class factors as 1.23.ai $\times$ 2.23.ap_dv 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 |
|---|---|---|
| 3.23.ah_c_dy | $2$ | (not in LMFDB) |
| 3.23.h_c_ady | $2$ | (not in LMFDB) |
| 3.23.x_ji_cfa | $2$ | (not in LMFDB) |