Invariants
| Base field: | $\F_{2^{10}}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 63 x + 1024 x^{2} )( 1 - 61 x + 1024 x^{2} )$ |
| $1 - 124 x + 5891 x^{2} - 126976 x^{3} + 1048576 x^{4}$ | |
| Frobenius angles: | $\pm0.0563432964760$, $\pm0.0978468837242$ |
| Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $927368$ | $1095748353024$ | $1152818322402162104$ | $1208923296386095001088000$ | $1267650549825516476473396268648$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $901$ | $1044983$ | $1073645725$ | $1099509332911$ | $1125899862076021$ | $1152921504141032231$ | $1180591620732745587469$ | $1208925819615996797697631$ | $1237940039285447319776129125$ | $1267650600228232093922623030103$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{10}}$.
Endomorphism algebra over $\F_{2^{10}}$| The isogeny class factors as 1.1024.acl $\times$ 1.1024.acj 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 |
|---|---|---|
| 2.1024.ac_acrb | $2$ | (not in LMFDB) |
| 2.1024.c_acrb | $2$ | (not in LMFDB) |
| 2.1024.eu_isp | $2$ | (not in LMFDB) |