Invariants
Base field: | $\F_{29}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 14 x + 93 x^{2} - 406 x^{3} + 841 x^{4}$ |
Frobenius angles: | $\pm0.0232315260076$, $\pm0.402168915073$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.203840.5 |
Galois group: | $D_{4}$ |
Jacobians: | $2$ |
Isomorphism classes: | 2 |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $515$ | $697825$ | $593430380$ | $498711103625$ | $420348118639075$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $16$ | $832$ | $24334$ | $705108$ | $20493636$ | $594765982$ | $17249866804$ | $500246330148$ | $14507137149766$ | $420707161799952$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+8x^5+19x^4+3x^3+15x^2+8x+14$
- $y^2=11x^6+19x^5+27x^4+23x^3+20x^2+5x+26$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{29}$.
Endomorphism algebra over $\F_{29}$The endomorphism algebra of this simple isogeny class is 4.0.203840.5. |
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 |
---|---|---|
2.29.o_dp | $2$ | (not in LMFDB) |