Invariants
Base field: | $\F_{193}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 948 x^{2} - 9264 x^{3} + 37249 x^{4}$ |
Frobenius angles: | $\pm0.0177587632772$, $\pm0.239932532337$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2722048.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28886$ | $1372373860$ | $51669078950918$ | $1925124687459859600$ | $71708862828564593649446$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $146$ | $36842$ | $7187186$ | $1387489254$ | $267785027186$ | $51682529681354$ | $9974730034518290$ | $1925122947729218686$ | $371548729845751675538$ | $71708904872657998588682$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=41x^6+10x^5+40x^4+120x^3+37x^2+21x+164$
- $y^2=101x^6+39x^5+100x^4+149x^3+21x^2+119x+32$
- $y^2=99x^6+169x^5+11x^4+45x^3+16x^2+81x+100$
- $y^2=4x^6+149x^5+33x^4+101x^3+190x^2+72x+143$
- $y^2=42x^6+172x^5+79x^4+133x^3+11x^2+163x+178$
- $y^2=21x^6+154x^5+177x^4+6x^3+102x^2+76x+51$
- $y^2=185x^6+54x^5+139x^4+180x^3+112x^2+73x+135$
- $y^2=125x^6+53x^5+150x^4+38x^3+160x^2+4x+123$
- $y^2=100x^6+113x^5+61x^4+62x^3+105x^2+148x+147$
- $y^2=19x^6+35x^5+121x^4+85x^3+16x^2+86x+65$
- $y^2=32x^6+74x^5+25x^4+132x^3+75x^2+143x+93$
- $y^2=136x^6+88x^5+122x^4+13x^3+62x^2+132x+52$
- $y^2=43x^6+73x^5+134x^4+32x^3+44x^2+70x+81$
- $y^2=141x^6+112x^5+20x^4+115x^3+137x^2+39x+66$
- $y^2=129x^6+89x^5+90x^4+121x^3+152x^2+155x+105$
- $y^2=164x^6+131x^5+82x^4+109x^3+37x^2+154x+42$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{193}$.
Endomorphism algebra over $\F_{193}$The endomorphism algebra of this simple isogeny class is 4.0.2722048.1. |
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 |
---|---|---|
2.193.bw_bkm | $2$ | (not in LMFDB) |