Invariants
Base field: | $\F_{11}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 11 x^{2} )( 1 - 10 x + 45 x^{2} - 110 x^{3} + 121 x^{4} )$ |
$1 - 15 x + 106 x^{2} - 445 x^{3} + 1166 x^{4} - 1815 x^{5} + 1331 x^{6}$ | |
Frobenius angles: | $\pm0.0820279942768$, $\pm0.228229222880$, $\pm0.318205720493$ |
Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $329$ | $1605191$ | $2465610224$ | $3196135929875$ | $4184414508938279$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-3$ | $109$ | $1392$ | $14909$ | $161327$ | $1770004$ | $19479877$ | $214351861$ | $2358006432$ | $25937764029$ |
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.af $\times$ 2.11.ak_bt 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.af_g_f | $2$ | (not in LMFDB) |
3.11.f_g_af | $2$ | (not in LMFDB) |
3.11.p_ec_rd | $2$ | (not in LMFDB) |