Invariants
Base field: | $\F_{53}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 22 x + 219 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
Frobenius angles: | $\pm0.101347056399$, $\pm0.310329881205$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.193088.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1841$ | $7763497$ | $22210177472$ | $62278904913449$ | $174885069917659801$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $32$ | $2764$ | $149186$ | $7892916$ | $418189752$ | $22164190102$ | $1174710607592$ | $62259702624804$ | $3299763793770362$ | $174887471993889084$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=26x^6+7x^5+7x^3+48x^2+16x+32$
- $y^2=33x^6+7x^5+3x^4+31x^3+4x^2+37x+48$
- $y^2=2x^6+45x^5+35x^4+38x^3+32x^2+30x+36$
- $y^2=20x^6+8x^5+9x^4+47x^3+24x^2+12x+19$
- $y^2=50x^6+36x^5+17x^4+35x^3+15x^2+7x+26$
- $y^2=12x^6+32x^5+5x^4+42x^3+40x^2+17x+4$
- $y^2=49x^6+32x^5+15x^4+22x^3+27x^2+26x+14$
- $y^2=2x^6+51x^5+35x^4+27x^3+52x^2+10x+20$
- $y^2=44x^6+39x^5+38x^4+35x^3+4x^2+4x+14$
- $y^2=21x^6+25x^5+39x^4+11x^3+19x^2+6x+8$
- $y^2=19x^6+51x^5+32x^4+42x^3+14x^2+4x+51$
- $y^2=27x^6+12x^5+17x^4+34x^3+19x^2+50x+40$
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 4.0.193088.1. |
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.w_il | $2$ | (not in LMFDB) |