Invariants
| Base field: | $\F_{383}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 34 x + 383 x^{2}$ |
| Frobenius angles: | $\pm0.164982070069$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-94}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $8$ |
| Isomorphism classes: | 8 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $350$ | $146300$ | $56181650$ | $21517804000$ | $8241269716750$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $350$ | $146300$ | $56181650$ | $21517804000$ | $8241269716750$ | $3156404539187900$ | $1208902897439142850$ | $463009808997788976000$ | $177332756837355226817150$ | $67918445868684218784861500$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):
- $y^2=x^3+317 x+53$
- $y^2=x^3+88 x+57$
- $y^2=x^3+327 x+103$
- $y^2=x^3+150 x+367$
- $y^2=x^3+44 x+44$
- $y^2=x^3+162 x+44$
- $y^2=x^3+59 x+59$
- $y^2=x^3+221 x+339$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{383}$.
Endomorphism algebra over $\F_{383}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-94}) \). |
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 |
|---|---|---|
| 1.383.bi | $2$ | (not in LMFDB) |