Invariants
Base field: | $\F_{17^{2}}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 30 x + 289 x^{2}$ |
Frobenius angles: | $\pm0.155958260755$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-1}) \) |
Galois group: | $C_2$ |
Jacobians: | $8$ |
This isogeny class is simple and geometrically simple, not primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $1$ |
Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $260$ | $83200$ | $24136580$ | $6975820800$ | $2015996087300$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $260$ | $83200$ | $24136580$ | $6975820800$ | $2015996087300$ | $582622284524800$ | $168377827346252420$ | $48661191885604147200$ | $14063084452138443271940$ | $4064231406646822197280000$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{17^{2}}$.
Endomorphism algebra over $\F_{17^{2}}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1}) \). |
Base change
This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{17^{2}}$.
Subfield | Primitive Model |
$\F_{17}$ | 1.17.ai |
$\F_{17}$ | 1.17.i |
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
1.289.be | $2$ | (not in LMFDB) |
1.289.aq | $4$ | (not in LMFDB) |
1.289.q | $4$ | (not in LMFDB) |