Invariants
| Base field: | $\F_{29}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 9 x + 29 x^{2} )( 1 - 8 x + 29 x^{2} )$ |
| $1 - 17 x + 130 x^{2} - 493 x^{3} + 841 x^{4}$ | |
| Frobenius angles: | $\pm0.185103371333$, $\pm0.233506187634$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $462$ | $684684$ | $600686856$ | $502229407680$ | $421048710399702$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $13$ | $813$ | $24628$ | $710081$ | $20527793$ | $594884106$ | $17249925797$ | $500245203361$ | $14507134949092$ | $420707176370853$ |
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 $\F_{29}$.
Endomorphism algebra over $\F_{29}$| The isogeny class factors as 1.29.aj $\times$ 1.29.ai 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 |
|---|---|---|
| 2.29.ab_ao | $2$ | (not in LMFDB) |
| 2.29.b_ao | $2$ | (not in LMFDB) |
| 2.29.r_fa | $2$ | (not in LMFDB) |