Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 7 x + 54 x^{2} - 161 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.303118196219$, $\pm0.452082776152$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.396797.1 |
Galois group: | $D_{4}$ |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $416$ | $312832$ | $151828352$ | $78299346944$ | $41402601057376$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $17$ | $589$ | $12476$ | $279801$ | $6432627$ | $148030462$ | $3404818637$ | $78310653969$ | $1801151802452$ | $41426524866309$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=17x^6+6x^5+4x^4+12x^3+7x^2+13x+15$
- $y^2=5x^6+5x^5+20x^3+3$
- $y^2=10x^6+8x^5+19x^4+14x^3+20x^2+20x+20$
- $y^2=6x^6+x^5+11x^4+22x^3+x^2+2x+16$
- $y^2=x^6+17x^5+17x^4+4x^3+17x^2+21x+7$
- $y^2=21x^6+2x^5+7x^3+20x^2+14x+5$
- $y^2=18x^6+7x^5+19x^4+21x^3+x^2+19x+15$
- $y^2=9x^6+20x^5+4x^4+9x^3+7x^2+18x+2$
- $y^2=22x^6+13x^5+18x^4+18x^3+19x^2+16x+4$
- $y^2=17x^6+x^5+17x^4+19x^3+16x^2+11x+5$
- $y^2=9x^6+2x^5+14x^4+4x^3+19x^2+7x+16$
- $y^2=14x^6+19x^4+21x^3+5x^2+18x+2$
- $y^2=2x^6+12x^5+20x^4+6x^3+5x^2+18x$
- $y^2=21x^6+22x^5+3x^4+12x^3+3x^2+6x+13$
- $y^2=11x^6+9x^5+22x^4+16x^3+11x^2+20x+22$
- $y^2=4x^6+18x^5+5x^4+4x^3+17x^2+12x$
- $y^2=10x^6+19x^5+6x^4+18x^2+11x+11$
- $y^2=12x^6+15x^5+7x^4+11x^3+7x^2+6x+3$
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 4.0.396797.1. |
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.h_cc | $2$ | (not in LMFDB) |