Invariants
Base field: | $\F_{11}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )$ |
$1 - 11 x + 52 x^{2} - 121 x^{3} + 121 x^{4}$ | |
Frobenius angles: | $\pm0.140218899004$, $\pm0.228229222880$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $42$ | $12852$ | $1802808$ | $218484000$ | $26131191702$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $1$ | $105$ | $1354$ | $14921$ | $162251$ | $1774962$ | $19493321$ | $214361041$ | $2357918014$ | $25937318505$ |
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 $\F_{11}$.
Endomorphism algebra over $\F_{11}$The isogeny class factors as 1.11.ag $\times$ 1.11.af 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 |
---|---|---|
2.11.ab_ai | $2$ | 2.121.ar_ky |
2.11.b_ai | $2$ | 2.121.ar_ky |
2.11.l_ca | $2$ | 2.121.ar_ky |