Invariants
| Base field: | $\F_{349}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 - 24 x + 349 x^{2}$ |
| Frobenius angles: | $\pm0.277961534775$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-205}) \) |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $326$ | $121924$ | $42519854$ | $14835712320$ | $5177585320886$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $326$ | $121924$ | $42519854$ | $14835712320$ | $5177585320886$ | $1806976695322084$ | $630634880026581854$ | $220091573652898970880$ | $76811959212766314501926$ | $26807373765262409484576004$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):
- $y^2=x^3+39 x+39$
- $y^2=x^3+337 x+337$
- $y^2=x^3+298 x+298$
- $y^2=x^3+71 x+71$
- $y^2=x^3+329 x+329$
- $y^2=x^3+19 x+38$
- $y^2=x^3+308 x+308$
- $y^2=x^3+343 x+337$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{349}$.
Endomorphism algebra over $\F_{349}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-205}) \). |
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 |
|---|---|---|
| 1.349.y | $2$ | (not in LMFDB) |