Invariants
Base field: | $\F_{53}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 21 x + 207 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
Frobenius angles: | $\pm0.119784165977$, $\pm0.328808403738$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.50653.1 |
Galois group: | $C_4$ |
Jacobians: | $13$ |
Isomorphism classes: | 13 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1883$ | $7816333$ | $22230059663$ | $62281111936309$ | $174885222759273488$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $33$ | $2783$ | $149319$ | $7893195$ | $418190118$ | $22164253319$ | $1174711769439$ | $62259712345555$ | $3299763817200321$ | $174887471562084038$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=32x^6+42x^4+39x^3+36x^2+26x+13$
- $y^2=32x^6+21x^5+43x^4+7x^3+14x^2+21x+48$
- $y^2=48x^6+49x^5+25x^4+31x^3+20x^2+32x+50$
- $y^2=48x^6+4x^5+43x^4+19x^3+41x^2+14x+35$
- $y^2=43x^6+26x^5+42x^4+25x^3+41x^2+27x+20$
- $y^2=46x^6+6x^5+46x^4+11x^3+19x^2+24x+38$
- $y^2=47x^6+49x^5+17x^4+19x^3+33x^2+15x+12$
- $y^2=45x^6+7x^5+21x^4+16x^3+41x^2+37x+51$
- $y^2=35x^6+52x^5+40x^4+32x^3+20x^2+16x+47$
- $y^2=37x^6+35x^5+x^4+34x^2+44x+31$
- $y^2=45x^6+51x^5+4x^4+21x^3+39x^2+42x+37$
- $y^2=x^6+17x^5+4x^4+10x^3+34x^2+28x+7$
- $y^2=30x^6+46x^5+48x^4+7x^2+41x+26$
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 4.0.50653.1. |
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_hz | $2$ | (not in LMFDB) |