Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 648 x^{2} - 5421 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0871410937773$, $\pm0.257078959530$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.793432.1 |
Galois group: | $D_{4}$ |
Jacobians: | $42$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14510$ | $368989300$ | $7213177710920$ | $139361428579060000$ | $2692462219392528300050$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $101$ | $19097$ | $2685854$ | $373321833$ | $51889037711$ | $7212549083762$ | $1002544338698549$ | $139353666910242193$ | $19370159744418549146$ | $2692452204315254169977$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 42 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=76x^6+137x^5+67x^4+36x^3+7x^2+115x+87$
- $y^2=85x^6+112x^5+35x^4+83x^3+91x^2+38x+126$
- $y^2=92x^6+29x^5+138x^4+47x^3+3x^2+9x+37$
- $y^2=33x^6+105x^5+70x^4+35x^3+117x^2+85x+124$
- $y^2=104x^6+118x^5+51x^4+66x^3+49x^2+67x+14$
- $y^2=57x^6+66x^5+48x^4+82x^3+97x^2+108x+138$
- $y^2=19x^6+35x^5+67x^4+135x^3+136x^2+68x+85$
- $y^2=122x^6+42x^5+54x^4+124x^3+135x^2+80x+6$
- $y^2=98x^6+124x^5+64x^4+32x^3+87x^2+69x+124$
- $y^2=85x^6+129x^5+26x^4+95x^2+14x+49$
- $y^2=111x^6+24x^5+94x^4+x^3+61x^2+133x+104$
- $y^2=40x^6+124x^5+118x^4+137x^3+86x^2+48x+75$
- $y^2=63x^6+36x^5+109x^4+136x^3+119x^2+106x+101$
- $y^2=40x^6+92x^5+82x^4+127x^3+133x^2+35x+137$
- $y^2=121x^6+56x^5+28x^4+121x^3+56x^2+81x+68$
- $y^2=73x^6+100x^5+38x^4+43x^3+94x^2+39x+75$
- $y^2=58x^6+98x^5+66x^4+21x^3+40x^2+45x+17$
- $y^2=120x^6+97x^5+68x^4+6x^3+79x^2+75x+59$
- $y^2=111x^6+97x^5+118x^4+100x^3+14x^2+103x+9$
- $y^2=6x^6+38x^5+58x^4+6x^3+130x^2+46x+103$
- and 22 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The endomorphism algebra of this simple isogeny class is 4.0.793432.1. |
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 |
---|---|---|
2.139.bn_yy | $2$ | (not in LMFDB) |