Invariants
| Base field: | $\F_{157}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 12 x + 157 x^{2}$ |
| Frobenius angles: | $\pm0.341053001856$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-1}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $7$ |
| Isomorphism classes: | 7 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $146$ | $24820$ | $3873818$ | $607593600$ | $95388621266$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $146$ | $24820$ | $3873818$ | $607593600$ | $95388621266$ | $14976064173460$ | $2351243243934458$ | $369145195372454400$ | $57955795562886157586$ | $9099059901092321634100$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 7 curves (of which 0 are hyperelliptic):
- $y^2=x^3+65 x+130$
- $y^2=x^3+32 x+64$
- $y^2=x^3+6 x$
- $y^2=x^3+36 x+72$
- $y^2=x^3+89 x+89$
- $y^2=x^3+103 x+103$
- $y^2=x^3+151 x+145$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1}) \). |
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 |
|---|---|---|
| 1.157.m | $2$ | (not in LMFDB) |
| 1.157.aw | $4$ | (not in LMFDB) |
| 1.157.w | $4$ | (not in LMFDB) |