Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 852 x^{2} - 7498 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0800016625006$, $\pm0.186669006544$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1159488.4 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $19878$ | $695054148$ | $18745614367038$ | $498317561750990544$ | $13239688202999662862238$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $118$ | $26158$ | $4328494$ | $705920470$ | $115064071018$ | $18755377087534$ | $3057125325046834$ | $498311414948783710$ | $81224760535684673686$ | $13239635966994105402238$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=141x^6+87x^5+38x^4+73x^3+38x^2+131x+65$
- $y^2=140x^6+56x^5+92x^4+94x^3+154x^2+118x+153$
- $y^2=87x^6+59x^5+44x^4+112x^3+144x^2+98x+114$
- $y^2=94x^6+6x^5+130x^4+75x^3+74x^2+14x+2$
- $y^2=75x^6+138x^5+19x^4+29x^3+56x^2+37x+41$
- $y^2=56x^6+52x^5+112x^4+101x^3+149x^2+72x+130$
- $y^2=56x^6+62x^5+77x^4+32x^3+48x^2+124x+67$
- $y^2=56x^6+46x^5+134x^4+141x^3+107x^2+159x+91$
- $y^2=58x^6+128x^5+87x^4+162x^3+117x^2+89x+120$
- $y^2=148x^6+127x^5+109x^4+66x^3+29x^2+71x+11$
- $y^2=99x^6+67x^5+107x^4+158x^3+33x^2+30x+73$
- $y^2=86x^6+122x^5+42x^4+156x^3+78x^2+117x+58$
- $y^2=31x^6+8x^5+149x^4+105x^3+91x^2+67x+120$
- $y^2=108x^6+106x^5+53x^4+90x^3+23x^2+121x+45$
- $y^2=48x^6+95x^5+139x^4+105x^3+57x^2+124x+92$
- $y^2=89x^6+91x^5+136x^4+58x^3+126x^2+72x+45$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is 4.0.1159488.4. |
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 |
---|---|---|
2.163.bu_bgu | $2$ | (not in LMFDB) |