Invariants
Base field: | $\F_{11^{2}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 20 x + 121 x^{2} )( 1 - 19 x + 121 x^{2} )$ |
$1 - 39 x + 622 x^{2} - 4719 x^{3} + 14641 x^{4}$ | |
Frobenius angles: | $\pm0.136777651826$, $\pm0.168181340661$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $10506$ | $210351132$ | $3137188255200$ | $45953897279889600$ | $672761889963021866106$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $83$ | $14365$ | $1770860$ | $214378321$ | $25937883203$ | $3138434913922$ | $379749905294843$ | $45949730473717921$ | $5559917316817969820$ | $672749994925449042205$ |
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.au $\times$ 1.121.at 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_afi | $2$ | (not in LMFDB) |
2.121.b_afi | $2$ | (not in LMFDB) |
2.121.bn_xy | $2$ | (not in LMFDB) |