Invariants
| Base field: | $\F_{431}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 16 x + 431 x^{2}$ |
| Frobenius angles: | $\pm0.374081947748$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-367}) \) |
| Galois group: | $C_2$ |
| Jacobians: | $18$ |
| Isomorphism classes: | 18 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $416$ | $186368$ | $80079584$ | $34507153408$ | $14872574188576$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $416$ | $186368$ | $80079584$ | $34507153408$ | $14872574188576$ | $6410082412697600$ | $2762745570720175456$ | $1190743340527927001088$ | $513210379738381762614944$ | $221193673666971077264611328$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which 0 are hyperelliptic):
- $y^2=x^3+131 x+55$
- $y^2=x^3+119 x+119$
- $y^2=x^3+395 x+395$
- $y^2=x^3+43 x+43$
- $y^2=x^3+379 x+67$
- $y^2=x^3+373 x+373$
- $y^2=x^3+318 x+71$
- $y^2=x^3+392 x+392$
- $y^2=x^3+242 x+401$
- $y^2=x^3+87 x+87$
- $y^2=x^3+46 x+322$
- $y^2=x^3+361 x+361$
- $y^2=x^3+291 x+291$
- $y^2=x^3+140 x+140$
- $y^2=x^3+97 x+97$
- $y^2=x^3+128 x+34$
- $y^2=x^3+81 x+136$
- $y^2=x^3+241 x+241$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{431}$.
Endomorphism algebra over $\F_{431}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-367}) \). |
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 |
|---|---|---|
| 1.431.q | $2$ | (not in LMFDB) |