Invariants
Base field: | $\F_{151}$ |
Dimension: | $1$ |
L-polynomial: | $1 + 18 x + 151 x^{2}$ |
Frobenius angles: | $\pm0.761604347806$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-70}) \) |
Galois group: | $C_2$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $170$ | $22780$ | $3440630$ | $519930720$ | $78502264250$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $170$ | $22780$ | $3440630$ | $519930720$ | $78502264250$ | $11853913082620$ | $1789940692639430$ | $270281037131268480$ | $40812436768660917770$ | $6162677950280739869500$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{151}$.
Endomorphism algebra over $\F_{151}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-70}) \). |
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 |
---|---|---|
1.151.as | $2$ | (not in LMFDB) |