Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4} )$ |
| $1 - 23 x + 241 x^{2} - 1472 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.112386341891$, $\pm0.135789939707$, $\pm0.314924263207$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4290$ | $135624060$ | $1808039324520$ | $21969744191881200$ | $266739205154465707950$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $483$ | $12214$ | $280543$ | $6438851$ | $148046004$ | $3404938769$ | $78312090383$ | $1801159729318$ | $41426540165163$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$| The isogeny class factors as 1.23.aj $\times$ 2.23.ao_do 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.af_al_hc | $2$ | (not in LMFDB) |
| 3.23.f_al_ahc | $2$ | (not in LMFDB) |
| 3.23.x_jh_ceq | $2$ | (not in LMFDB) |