Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 12 x + 74 x^{2} - 276 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.127841060579$, $\pm0.392728894411$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.18432.2 |
Galois group: | $C_4$ |
Jacobians: | $14$ |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $316$ | $281872$ | $149359612$ | $78256687104$ | $41407899346876$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $12$ | $534$ | $12276$ | $279646$ | $6433452$ | $148043382$ | $3405018132$ | $78312048574$ | $1801154760012$ | $41426506930134$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=6x^6+4x^4+11x^3+19x^2+18x+11$
- $y^2=10x^6+7x^4+x^3+19x^2+4x+3$
- $y^2=18x^6+20x^5+21x^3+12x^2+5x+7$
- $y^2=14x^6+4x^5+18x^4+13x^3+16x^2+13x+12$
- $y^2=19x^6+9x^5+18x^3+9x^2+16x+5$
- $y^2=22x^6+17x^5+19x^4+20x^3+11x^2+16x+22$
- $y^2=7x^6+17x^5+6x^4+7x^3+11x^2+22x+14$
- $y^2=14x^6+9x^5+8x^4+21x^3+3x^2+10$
- $y^2=7x^6+14x^5+4x^4+4x^3+5x^2+22x+13$
- $y^2=11x^6+7x^5+17x^4+8x^3+4x^2+12x+6$
- $y^2=2x^6+6x^5+20x^4+9x^3+5x^2+x+22$
- $y^2=20x^6+14x^5+x^4+21x^3+3x^2+6x+11$
- $y^2=9x^6+3x^5+14x^4+4x^3+19x^2+22x+20$
- $y^2=10x^6+5x^5+7x^4+5x^3+21x^2+16x+9$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The endomorphism algebra of this simple isogeny class is 4.0.18432.2. |
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 |
---|---|---|
2.23.m_cw | $2$ | (not in LMFDB) |