Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 802 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0750186375807$, $\pm0.229660133188$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.161792.1 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20156$ | $697155728$ | $18751750366172$ | $498325665071335424$ | $13239675856885541673276$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26238$ | $4329912$ | $705931950$ | $115063963720$ | $18755371466094$ | $3057125213257032$ | $498311413523691870$ | $81224760525652025112$ | $13239635967043734342238$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=33x^6+2x^5+47x^4+143x^3+144x^2+13x+61$
- $y^2=62x^6+75x^5+28x^4+77x^3+21x^2+130x+5$
- $y^2=124x^6+143x^5+102x^4+41x^3+20x^2+142x+40$
- $y^2=127x^6+68x^5+30x^4+91x^3+86x^2+116x+51$
- $y^2=3x^6+96x^5+159x^4+122x^3+110x^2+128x+104$
- $y^2=19x^6+116x^5+152x^4+75x^3+75x^2+121x+131$
- $y^2=45x^6+80x^5+6x^4+88x^2+44x+2$
- $y^2=71x^6+107x^5+149x^4+104x^3+52x^2+54x+92$
- $y^2=98x^6+88x^5+157x^4+22x^3+162x^2+18x+70$
- $y^2=117x^6+82x^5+114x^4+162x^3+105x^2+66x+47$
- $y^2=141x^6+133x^5+39x^4+106x^3+162x^2+156x+44$
- $y^2=151x^6+15x^5+52x^4+67x^3+113x^2+131x+53$
- $y^2=30x^6+75x^5+158x^4+143x^3+156x^2+95x+75$
- $y^2=156x^6+155x^5+80x^4+57x^3+78x^2+119x+88$
- $y^2=120x^6+60x^5+37x^4+139x^3+95x^2+82x+110$
- $y^2=75x^6+106x^5+122x^4+86x^3+20x^2+155x+53$
- $y^2=98x^6+94x^5+40x^4+137x^3+141x^2+155x+158$
- $y^2=11x^6+48x^5+162x^4+50x^3+74x^2+81x+110$
- $y^2=7x^6+55x^5+33x^4+150x^3+47x^2+91x+81$
- $y^2=77x^6+25x^5+94x^4+19x^3+16x^2+4x+11$
- $y^2=129x^6+149x^5+113x^4+106x^3+21x^2+12x+15$
- $y^2=38x^6+98x^5+150x^4+140x^3+89x^2+134x+116$
- $y^2=56x^6+82x^5+81x^4+72x^3+109x^2+123x+114$
- $y^2=158x^6+41x^5+34x^4+129x^3+70x^2+71x+24$
- $y^2=28x^6+108x^5+132x^3+40x^2+58x+23$
- $y^2=141x^6+55x^5+32x^4+21x^3+66x^2+6x+118$
- $y^2=69x^6+17x^5+55x^4+41x^3+45x^2+160x+22$
- $y^2=39x^6+6x^5+46x^4+20x^3+22x^2+84x+92$
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 4.0.161792.1. |
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.bs_bew | $2$ | (not in LMFDB) |