Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 31 x + 243 x^{2} )( 1 - 29 x + 243 x^{2} )$ |
$1 - 60 x + 1385 x^{2} - 14580 x^{3} + 59049 x^{4}$ | |
Frobenius angles: | $\pm0.0339262533067$, $\pm0.119654564389$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $45795$ | $3438059625$ | $205741381552560$ | $12157262903676515625$ | $717897118120360293788475$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $184$ | $58220$ | $14338468$ | $3486668948$ | $847287583144$ | $205891127215910$ | $50031545160853048$ | $12157665461379173348$ | $2954312706593971455004$ | $717897987692414451871100$ |
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.abf $\times$ 1.243.abd 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.ac_apx | $2$ | (not in LMFDB) |
2.243.c_apx | $2$ | (not in LMFDB) |
2.243.ci_cbh | $2$ | (not in LMFDB) |