Invariants
Base field: | $\F_{11^{2}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 19 x + 121 x^{2} )( 1 - 18 x + 121 x^{2} )$ |
$1 - 37 x + 584 x^{2} - 4477 x^{3} + 14641 x^{4}$ | |
Frobenius angles: | $\pm0.168181340661$, $\pm0.194982229042$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $10712$ | $211454880$ | $3139742902400$ | $45957807461704320$ | $672765656169997676312$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $85$ | $14441$ | $1772302$ | $214396561$ | $25938028405$ | $3138434968718$ | $379749882720685$ | $45949729983499681$ | $5559917309905369342$ | $672749994853283357801$ |
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 $\F_{11^{2}}$.
Endomorphism algebra over $\F_{11^{2}}$The isogeny class factors as 1.121.at $\times$ 1.121.as 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 |
---|---|---|
2.121.ab_adw | $2$ | (not in LMFDB) |
2.121.b_adw | $2$ | (not in LMFDB) |
2.121.bl_wm | $2$ | (not in LMFDB) |