Invariants
Base field: | $\F_{439}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 20 x + 439 x^{2}$ |
Frobenius angles: | $\pm0.341624939565$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-339}) \) |
Galois group: | $C_2$ |
Jacobians: | $24$ |
This isogeny class is simple and geometrically simple, 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $420$ | $193200$ | $84622860$ | $37141540800$ | $16305062594100$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $420$ | $193200$ | $84622860$ | $37141540800$ | $16305062594100$ | $7157924468074800$ | $3142328913675658140$ | $1379482393674142867200$ | $605592770802667526998980$ | $265855226381714958312030000$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{439}$.
Endomorphism algebra over $\F_{439}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-339}) \). |
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 |
---|---|---|
1.439.u | $2$ | (not in LMFDB) |