Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 43 x + 780 x^{2} - 7009 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0963982022717$, $\pm0.239744545163$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.19262232.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20298$ | $698291796$ | $18755743913784$ | $498335420686303776$ | $13239694889809631911398$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $121$ | $26281$ | $4330834$ | $705945769$ | $115064129131$ | $18755373353506$ | $3057125240204065$ | $498311414015429713$ | $81224760534483718438$ | $13239635967173948241721$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=120x^6+142x^5+94x^4+76x^3+105x^2+113x+114$
- $y^2=5x^6+117x^5+152x^4+159x^3+80x^2+96x+98$
- $y^2=79x^6+41x^5+58x^4+21x^3+74x^2+131x+24$
- $y^2=119x^6+3x^5+11x^4+159x^3+138x^2+48$
- $y^2=102x^6+54x^5+133x^4+150x^3+141x^2+13x+13$
- $y^2=123x^6+123x^5+74x^4+50x^3+135x^2+136x+110$
- $y^2=134x^6+12x^5+130x^4+138x^3+59x^2+9x+8$
- $y^2=7x^6+94x^5+28x^4+47x^3+56x^2+60x+110$
- $y^2=58x^6+32x^5+19x^4+25x^3+12x^2+95x+139$
- $y^2=98x^6+52x^5+9x^4+140x^3+86x^2+53x+83$
- $y^2=68x^6+115x^5+117x^4+112x^3+67x^2+32x+90$
- $y^2=158x^6+33x^5+95x^4+30x^3+96x^2+80x+159$
- $y^2=28x^6+153x^5+48x^4+151x^3+52x^2+119x+93$
- $y^2=117x^6+82x^5+162x^4+7x^3+142x^2+157x+93$
- $y^2=108x^6+52x^5+112x^4+139x^3+120x^2+87x+102$
- $y^2=153x^6+150x^5+154x^4+151x^3+12x^2+15x+55$
- $y^2=123x^5+76x^4+11x^3+32x^2+46x+68$
- $y^2=71x^6+48x^5+117x^4+146x^3+71x^2+20x+65$
- $y^2=3x^6+37x^5+105x^4+155x^3+117x^2+96x+56$
- $y^2=120x^6+50x^5+157x^4+52x^3+62x^2+15x$
- $y^2=48x^6+89x^5+64x^4+107x^3+145x^2+59x+5$
- $y^2=84x^6+101x^5+43x^4+111x^3+3x^2+55x+112$
- $y^2=100x^6+150x^5+36x^4+124x^3+2x^2+47x+3$
- $y^2=63x^6+123x^5+118x^4+135x^3+114x^2+2x+142$
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 4.0.19262232.1. |
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 |
---|---|---|
2.163.br_bea | $2$ | (not in LMFDB) |