Invariants
| Base field: | $\F_{53}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 21 x + 201 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
| Frobenius angles: | $\pm0.0465014224412$, $\pm0.350375930745$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2816797.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $7$ |
| Isomorphism classes: | 7 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1877$ | $7780165$ | $22173505913$ | $62236223991925$ | $174862566037320272$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $33$ | $2771$ | $148941$ | $7887507$ | $418135938$ | $22163888099$ | $1174709688801$ | $62259697089763$ | $3299763664516293$ | $174887470263891686$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+46x^5+45x^4+15x^3+38x^2+5x+8$
- $y^2=40x^6+11x^5+7x^4+4x^3+22x^2+32x+2$
- $y^2=41x^6+38x^5+10x^4+31x^3+24x^2+24x+49$
- $y^2=43x^6+29x^5+3x^4+50x^3+35x^2+10x+13$
- $y^2=34x^6+40x^5+42x^4+35x^3+16x^2+43x+18$
- $y^2=27x^6+52x^5+22x^4+19x^3+43x^2+10x+12$
- $y^2=50x^6+17x^5+6x^4+47x^3+10x+50$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{53}$.
Endomorphism algebra over $\F_{53}$| The endomorphism algebra of this simple isogeny class is 4.0.2816797.1. |
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 |
|---|---|---|
| 2.53.v_ht | $2$ | (not in LMFDB) |