Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 33 x^{2} - 88 x^{3} + 121 x^{4} )$ |
$1 - 14 x + 92 x^{2} - 374 x^{3} + 1012 x^{4} - 1694 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.110710227191$, $\pm0.140218899004$, $\pm0.414323386517$ |
Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $354$ | $1599372$ | $2356790400$ | $3115026472032$ | $4172746362504834$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $110$ | $1330$ | $14530$ | $160878$ | $1775096$ | $19511098$ | $214429570$ | $2358046870$ | $25937536030$ |
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 $\times$ 2.11.ai_bh 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 |
---|---|---|
3.11.ac_ae_w | $2$ | (not in LMFDB) |
3.11.c_ae_aw | $2$ | (not in LMFDB) |
3.11.o_do_ok | $2$ | (not in LMFDB) |