Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 12 x + 79 x^{2} - 276 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.201562474799$, $\pm0.353216304931$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.342288.1 |
Galois group: | $D_{4}$ |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $321$ | $287937$ | $151580052$ | $78634730889$ | $41434923729201$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $12$ | $544$ | $12456$ | $280996$ | $6437652$ | $148032502$ | $3404847612$ | $78311269444$ | $1801152693432$ | $41426497057984$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=7x^6+19x^5+16x^4+11x^3+12x^2+6x+22$
- $y^2=19x^6+20x^5+11x^4+3x^3+17x^2+4$
- $y^2=8x^6+18x^5+3x^4+6x^3+18x^2+3x+20$
- $y^2=12x^6+5x^5+18x^4+19x^3+3x^2+5x+18$
- $y^2=5x^6+21x^5+4x^4+15x^3+14x^2+10x+14$
- $y^2=14x^6+14x^5+16x^4+14x^3+9x^2+11x+2$
- $y^2=14x^6+8x^5+x^4+22x^3+11x^2+2x+16$
- $y^2=10x^6+3x^5+20x^3+21x^2+21x+5$
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 4.0.342288.1. |
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_db | $2$ | (not in LMFDB) |