Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 33 x^{2} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.187321230621$, $\pm0.812678769379$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-53}, \sqrt{119})\) |
| Galois group: | $C_2^2$ |
| Jacobians: | $20$ |
| Isomorphism classes: | 48 |
This isogeny class is simple but not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1817$ | $3301489$ | $6321510164$ | $11706053230921$ | $21611482042284257$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $44$ | $1784$ | $79508$ | $3424020$ | $147008444$ | $6321657278$ | $271818611108$ | $11688200339044$ | $502592611936844$ | $21611481771284264$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):
- $y^2=20 x^6+21 x^5+13 x^4+39 x^3+18 x^2+7 x+28$
- $y^2=17 x^6+20 x^5+39 x^4+31 x^3+11 x^2+21 x+41$
- $y^2=8 x^6+2 x^5+24 x^4+5 x^3+6 x^2+6 x+25$
- $y^2=3 x^6+40 x^5+14 x^4+16 x^3+14 x^2+41 x+11$
- $y^2=9 x^6+34 x^5+42 x^4+5 x^3+42 x^2+37 x+33$
- $y^2=28 x^6+16 x^5+31 x^4+39 x^3+40 x^2+21 x+28$
- $y^2=2 x^6+24 x^5+18 x^4+30 x^2+42 x+10$
- $y^2=19 x^6+7 x^5+11 x^4+15 x^3+42 x^2+33 x+12$
- $y^2=6 x^6+41 x^5+20 x^4+39 x^3+15 x^2+28 x+11$
- $y^2=18 x^6+37 x^5+17 x^4+31 x^3+2 x^2+41 x+33$
- $y^2=30 x^6+20 x^5+42 x^4+7 x^3+9 x^2+36 x+10$
- $y^2=4 x^6+17 x^5+40 x^4+21 x^3+27 x^2+22 x+30$
- $y^2=15 x^6+14 x^5+14 x^4+33 x^3+38 x^2+13 x+20$
- $y^2=2 x^6+42 x^5+42 x^4+13 x^3+28 x^2+39 x+17$
- $y^2=30 x^6+22 x^5+10 x^4+18 x^3+7 x^2+22 x+21$
- $y^2=4 x^6+23 x^5+30 x^4+11 x^3+21 x^2+23 x+20$
- $y^2=39 x^6+41 x^5+29 x^4+37 x^3+11 x^2+14 x+5$
- $y^2=31 x^6+37 x^5+x^4+25 x^3+33 x^2+42 x+15$
- $y^2=10 x^6+26 x^5+33 x^4+37 x^3+21 x^2+30 x+32$
- $y^2=30 x^6+35 x^5+13 x^4+25 x^3+20 x^2+4 x+10$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{43^{2}}$.
Endomorphism algebra over $\F_{43}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-53}, \sqrt{119})\). |
| The base change of $A$ to $\F_{43^{2}}$ is 1.1849.abh 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-6307}) \)$)$ |
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.a_bh | $4$ | (not in LMFDB) |