Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 693 x^{2} - 5699 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0825424652016$, $\pm0.219145610075$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3618405.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14275$ | $367652625$ | $7210459053925$ | $139359685241338125$ | $2692468381320814102000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $19027$ | $2684841$ | $373317163$ | $51889156464$ | $7212552283807$ | $1002544376998011$ | $139353667038909763$ | $19370159739738453309$ | $2692452204199932910102$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=132x^6+128x^5+106x^4+75x^3+109x^2+60x+65$
- $y^2=95x^6+21x^5+36x^4+112x^3+52x^2+76x+73$
- $y^2=26x^6+37x^5+110x^4+3x^3+56x^2+83x+4$
- $y^2=73x^6+118x^5+11x^4+115x^3+16x^2+96x+99$
- $y^2=29x^6+71x^5+69x^4+67x^3+26x^2+7x+27$
- $y^2=39x^6+65x^5+43x^4+94x^3+62x^2+118x+14$
- $y^2=54x^6+96x^5+115x^4+7x^3+64x^2+19x+38$
- $y^2=82x^6+105x^5+91x^4+39x^3+132x^2+125x+87$
- $y^2=134x^6+120x^5+111x^4+109x^3+101x^2+64x+49$
- $y^2=x^6+115x^5+9x^4+10x^3+73x^2+29x+59$
- $y^2=89x^6+69x^5+24x^4+68x^3+132x^2+100x+62$
- $y^2=60x^6+74x^5+69x^4+111x^3+16x^2+74x+83$
- $y^2=105x^6+51x^5+33x^4+39x^3+102x^2+73x+87$
- $y^2=56x^6+7x^5+108x^4+45x^3+75x^2+97x+102$
- $y^2=40x^6+126x^5+64x^4+54x^3+81x^2+128x+8$
- $y^2=69x^6+93x^5+26x^4+19x^3+44x^2+130x+88$
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 4.0.3618405.2. |
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.bp_bar | $2$ | (not in LMFDB) |