Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 63 x + 1024 x^{2} )( 1 - 59 x + 1024 x^{2} )$ |
$1 - 122 x + 5765 x^{2} - 124928 x^{3} + 1048576 x^{4}$ | |
Frobenius angles: | $\pm0.0563432964760$, $\pm0.126656933887$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $929292$ | $1095999550464$ | $1152834919429745916$ | $1208924116004855258910720$ | $1267650583102074686927394015852$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $903$ | $1045223$ | $1073661183$ | $1099510078351$ | $1125899891631543$ | $1152921505126015991$ | $1180591620759434385327$ | $1208925819616487382197791$ | $1237940039285445521868036327$ | $1267650600228231354532129156103$ |
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.ach 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.ae_acmf | $2$ | (not in LMFDB) |
2.1024.e_acmf | $2$ | (not in LMFDB) |
2.1024.es_int | $2$ | (not in LMFDB) |