Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 17 x + 73 x^{2} )( 1 - 16 x + 73 x^{2} )$ |
$1 - 33 x + 418 x^{2} - 2409 x^{3} + 5329 x^{4}$ | |
Frobenius angles: | $\pm0.0323195869136$, $\pm0.114200251220$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 3 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3306$ | $27076140$ | $150642478728$ | $806141165356800$ | $4297502623382655546$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $41$ | $5077$ | $387236$ | $28387009$ | $2073012161$ | $151334015794$ | $11047398851705$ | $806460107544001$ | $58871586895319108$ | $4297625831257564357$ |
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 $\F_{73}$.
Endomorphism algebra over $\F_{73}$The isogeny class factors as 1.73.ar $\times$ 1.73.aq 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.