Invariants
| Base field: | $\F_{43}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 12 x + 74 x^{2} - 516 x^{3} + 1849 x^{4}$ |
| Frobenius angles: | $\pm0.0537701446523$, $\pm0.522547179182$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.29952.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1396$ | $3422992$ | $6272921812$ | $11666213950464$ | $21610351682932276$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $32$ | $1854$ | $78896$ | $3412366$ | $147000752$ | $6321423822$ | $271817720192$ | $11688193020574$ | $502592636361152$ | $21611482571315934$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):
- $y^2=35 x^6+29 x^5+6 x^4+25 x^3+37 x^2+x+16$
- $y^2=25 x^6+40 x^5+33 x^4+21 x^3+28 x^2+6 x+26$
- $y^2=18 x^6+30 x^5+11 x^4+30 x^3+4 x^2+x+12$
- $y^2=8 x^6+25 x^5+21 x^4+28 x^3+40 x^2+3 x+34$
- $y^2=4 x^6+9 x^5+3 x^4+7 x^3+22 x^2+32 x+38$
- $y^2=25 x^6+10 x^5+11 x^4+20 x^3+3 x^2+40 x+3$
- $y^2=31 x^6+9 x^4+38 x^3+9 x^2+36 x+25$
- $y^2=11 x^6+19 x^5+10 x^4+13 x^3+24 x^2+35 x+24$
- $y^2=32 x^6+32 x^5+38 x^4+2 x^2+36 x+10$
- $y^2=19 x^6+14 x^5+7 x^4+37 x^3+6 x^2+39 x+12$
- $y^2=26 x^6+17 x^5+28 x^4+7 x^3+36 x^2+13 x+39$
- $y^2=12 x^6+2 x^5+2 x^4+16 x^3+6 x^2+31 x+20$
- $y^2=5 x^6+13 x^5+41 x^4+11 x^3+5 x^2+8 x+11$
- $y^2=32 x^6+25 x^5+15 x^4+40 x^3+12 x^2+19 x+17$
- $y^2=11 x^6+12 x^5+5 x^4+33 x^3+25 x^2+16 x+29$
- $y^2=27 x^6+36 x^5+23 x^4+13 x^3+11 x^2+2 x+8$
- $y^2=40 x^6+20 x^5+8 x^4+5 x^2+7 x$
- $y^2=39 x^6+4 x^5+26 x^4+26 x^3+14 x^2+3 x+36$
- $y^2=33 x^6+37 x^5+16 x^4+23 x^3+35 x^2+26 x+31$
- $y^2=3 x^6+21 x^5+5 x^4+38 x^3+6 x^2+21 x+29$
- $y^2=21 x^6+16 x^5+15 x^4+3 x^3+38 x^2+27 x+18$
- $y^2=6 x^6+39 x^5+12 x^4+14 x^3+13 x^2+41 x+4$
- $y^2=26 x^5+8 x^4+13 x^3+24 x^2+29 x+30$
- $y^2=8 x^6+39 x^5+4 x^4+38 x^3+26 x^2+6 x+22$
- $y^2=27 x^6+30 x^5+7 x^4+38 x^3+8 x^2+8 x+4$
- $y^2=32 x^6+23 x^5+21 x^4+34 x^3+27 x^2+17 x+32$
- $y^2=39 x^6+17 x^5+17 x^4+19 x^3+23 x^2+x+30$
- $y^2=40 x^6+25 x^5+22 x^4+24 x^3+7 x^2+8 x+34$
- $y^2=19 x^6+21 x^5+31 x^4+3 x^3+12 x^2+38 x+38$
- $y^2=16 x^6+10 x^5+3 x^4+42 x^3+34 x^2+4 x+7$
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 4.0.29952.1. |
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.m_cw | $2$ | (not in LMFDB) |