Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 29 x + 243 x^{2} )( 1 - 25 x + 243 x^{2} )$ |
$1 - 54 x + 1211 x^{2} - 13122 x^{3} + 59049 x^{4}$ | |
Frobenius angles: | $\pm0.119654564389$, $\pm0.203835764481$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $47085$ | $3457781145$ | $205881854255280$ | $12157982239610414025$ | $717900018650455667423925$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $190$ | $58556$ | $14348260$ | $3486875252$ | $847291006450$ | $205891172180774$ | $50031545591273590$ | $12157665463184333348$ | $2954312706562039184860$ | $717897987691551970464236$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{3^{5}}$.
Endomorphism algebra over $\F_{3^{5}}$The isogeny class factors as 1.243.abd $\times$ 1.243.az 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 |
---|---|---|
2.243.ae_ajf | $2$ | (not in LMFDB) |
2.243.e_ajf | $2$ | (not in LMFDB) |
2.243.cc_bup | $2$ | (not in LMFDB) |