Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 6 x + 14 x^{2} - 20 x^{3} + 35 x^{4} - 100 x^{5} + 350 x^{6} - 750 x^{7} + 625 x^{8}$ |
| Frobenius angles: | $\pm0.0821969324612$, $\pm0.124265393716$, $\pm0.434613314811$, $\pm0.771849011366$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 8.0.268960000.3 |
| Galois group: | $D_4\times C_2$ |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $149$ | $283249$ | $203948816$ | $149868462145$ | $89870250043589$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $18$ | $102$ | $614$ | $2940$ | $15978$ | $79492$ | $391494$ | $1957710$ | $9768578$ |
Jacobians and polarizations
It is unknown whether this isogeny class contains a Jacobian or whether it is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{5}$.
Endomorphism algebra over $\F_{5}$| The endomorphism algebra of this simple isogeny class is 8.0.268960000.3. |
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 |
|---|---|---|
| 4.5.g_o_u_bj | $2$ | (not in LMFDB) |
| 4.5.ac_g_au_bj | $4$ | (not in LMFDB) |
| 4.5.c_g_u_bj | $4$ | (not in LMFDB) |