Invariants
Base field: | $\F_{43}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 11 x + 43 x^{2} )( 1 - 8 x + 43 x^{2} )$ |
$1 - 19 x + 174 x^{2} - 817 x^{3} + 1849 x^{4}$ | |
Frobenius angles: | $\pm0.183291501244$, $\pm0.291171725172$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $12$ |
Isomorphism classes: | 56 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1188$ | $3397680$ | $6369908688$ | $11707657790400$ | $21615418248855948$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $25$ | $1837$ | $80116$ | $3424489$ | $147035215$ | $6321402934$ | $271818232837$ | $11688197507281$ | $502592608205548$ | $21611482341632557$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=26x^6+19x^5+19x^4+20x^3+17x^2+35x+19$
- $y^2=7x^6+x^5+3x^4+26x^3+6x^2+41x+14$
- $y^2=7x^6+14x^5+12x^4+4x^3+26x^2+40x+33$
- $y^2=27x^6+20x^5+29x^4+20x^3+12x^2+16x+27$
- $y^2=2x^6+35x^5+32x^4+16x^3+16x^2+24x+40$
- $y^2=17x^6+13x^5+22x^4+39x^3+18x^2+5x+27$
- $y^2=22x^6+14x^5+27x^4+13x^3+24x^2+7x+39$
- $y^2=34x^6+11x^5+19x^4+27x^3+32x^2+17x+20$
- $y^2=30x^6+10x^5+24x^3+8x^2+41x+23$
- $y^2=5x^6+2x^5+41x^4+35x^3+12x^2+32x+29$
- $y^2=32x^6+26x^5+33x^4+4x^3+17x^2+38x+18$
- $y^2=3x^6+8x^5+5x^4+22x^3+36x^2+6x+22$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43}$.
Endomorphism algebra over $\F_{43}$The isogeny class factors as 1.43.al $\times$ 1.43.ai and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.