Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 + x + 7 x^{2} + 5 x^{3} + 27 x^{4} + 11 x^{5} + 81 x^{6} + 45 x^{7} + 189 x^{8} + 81 x^{9} + 243 x^{10}$ |
| Frobenius angles: | $\pm0.228503896346$, $\pm0.440029839259$, $\pm0.488515155577$, $\pm0.686691898357$, $\pm0.752115552815$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.1495458993291875.1 |
| Galois group: | $C_2 \wr S_5$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $5$ |
| Slopes: | $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $691$ | $279855$ | $12198223$ | $4154447475$ | $786464843111$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $5$ | $23$ | $23$ | $99$ | $225$ | $779$ | $2413$ | $6099$ | $19013$ | $59463$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{3}$.
Endomorphism algebra over $\F_{3}$| The endomorphism algebra of this simple isogeny class is 10.0.1495458993291875.1. |
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 |
|---|---|---|
| 5.3.ab_h_af_bb_al | $2$ | (not in LMFDB) |