Invariants
Base field: | $\F_{43}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 20 x + 179 x^{2} - 860 x^{3} + 1849 x^{4}$ |
Frobenius angles: | $\pm0.0853946760970$, $\pm0.310510497030$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1117200.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1149$ | $3342441$ | $6334027956$ | $11691327169881$ | $21610086049060989$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $24$ | $1808$ | $79668$ | $3419716$ | $146998944$ | $6321224702$ | $271818034848$ | $11688203656708$ | $502592681255724$ | $21611482855023728$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=28x^6+34x^5+37x^4+34x^3+39x^2+7x+17$
- $y^2=37x^6+40x^5+31x^4+9x^3+37x^2+42x+6$
- $y^2=33x^6+16x^5+24x^4+5x^3+17x^2+3$
- $y^2=17x^6+22x^5+16x^4+42x^3+25x^2+19x+8$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$The endomorphism algebra of this simple isogeny class is 4.0.1117200.1. |
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 |
---|---|---|
2.43.u_gx | $2$ | (not in LMFDB) |