Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 7 x + 32 x^{2} - 161 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.144251603801$, $\pm0.554137439366$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.17375400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 24 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $394$ | $287620$ | $146191336$ | $78152106400$ | $41471996376094$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $17$ | $545$ | $12014$ | $279273$ | $6443407$ | $148070810$ | $3404833729$ | $78311363953$ | $1801156932962$ | $41426511857225$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=5x^6+7x^5+21x^3+10x^2+5x+13$
- $y^2=15x^6+18x^5+13x^4+4x^3+16x+6$
- $y^2=x^6+15x^5+19x^4+2x^3+14x^2+15x+21$
- $y^2=5x^6+16x^5+6x^4+5x^3+19x^2+13x+13$
- $y^2=5x^6+3x^5+21x^4+17x^3+14x^2+20x+8$
- $y^2=14x^6+9x^5+6x^4+6x^3+16x^2+17$
- $y^2=17x^6+2x^5+19x^4+6x^3+19x^2+18x+14$
- $y^2=4x^6+16x^5+14x^4+20x^3+5x^2+x+12$
- $y^2=5x^6+12x^5+9x^4+22x^3+5x^2+7$
- $y^2=22x^6+17x^5+21x^4+15x^3+x^2+9x+6$
- $y^2=15x^6+19x^5+x^4+7x^3+9x^2+17x+20$
- $y^2=22x^6+2x^5+10x^4+2x^3+21x^2+5x+7$
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 4.0.17375400.1. |
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_bg | $2$ | (not in LMFDB) |