Invariants
| Base field: | $\F_{23}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4} )$ |
| $1 - 22 x + 220 x^{2} - 1318 x^{3} + 5060 x^{4} - 11638 x^{5} + 12167 x^{6}$ | |
| Frobenius angles: | $\pm0.0682102518540$, $\pm0.112386341891$, $\pm0.376537722378$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4470$ | $136004220$ | $1788990337440$ | $21845982486952800$ | $266379289777152535350$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $486$ | $12086$ | $278962$ | $6430162$ | $148025016$ | $3404956942$ | $78312156386$ | $1801157202314$ | $41426520561846$ |
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.aj $\times$ 2.23.an_dc 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.ae_ao_es | $2$ | (not in LMFDB) |
| 3.23.e_ao_aes | $2$ | (not in LMFDB) |
| 3.23.w_im_bys | $2$ | (not in LMFDB) |