Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 3 x + 5 x^{2} )( 1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6} )$ |
| $1 - 11 x + 61 x^{2} - 221 x^{3} + 575 x^{4} - 1105 x^{5} + 1525 x^{6} - 1375 x^{7} + 625 x^{8}$ | |
| Frobenius angles: | $\pm0.0657033817182$, $\pm0.238557099512$, $\pm0.265942140215$, $\pm0.475140873389$ |
| Angle rank: | $4$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $75$ | $412425$ | $285123600$ | $156154415625$ | $96915522862875$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-5$ | $27$ | $145$ | $643$ | $3175$ | $15747$ | $77555$ | $387363$ | $1948690$ | $9773827$ |
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 $\F_{5}$.
Endomorphism algebra over $\F_{5}$| The isogeny class factors as 1.5.ad $\times$ 3.5.ai_bg_adh 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 |
|---|---|---|
| 4.5.af_n_abd_cn | $2$ | (not in LMFDB) |
| 4.5.f_n_bd_cn | $2$ | (not in LMFDB) |
| 4.5.l_cj_in_wd | $2$ | (not in LMFDB) |