Invariants
| Base field: | $\F_{5^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 3 x + 14 x^{2} + 179 x^{3} + 350 x^{4} + 1875 x^{5} + 15625 x^{6}$ |
| Frobenius angles: | $\pm0.289122521128$, $\pm0.484425495063$, $\pm0.914320774425$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1843390267595696.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 2748 |
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: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $18047$ | $251448851$ | $3923225202416$ | $59495198225882795$ | $931412770370049920327$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $29$ | $645$ | $16064$ | $389909$ | $9766569$ | $244150908$ | $6103364121$ | $152587165221$ | $3814693893008$ | $95367484869845$ |
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 $\F_{5^{2}}$.
Endomorphism algebra over $\F_{5^{2}}$| The endomorphism algebra of this simple isogeny class is 6.0.1843390267595696.1. |
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 |
|---|---|---|
| 3.25.ad_o_agx | $2$ | (not in LMFDB) |