Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 647 x^{2} - 5421 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0791680831941$, $\pm0.259916372902$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.248725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $33$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14509$ | $368949361$ | $7212862927831$ | $139360124139480189$ | $2692458526190717697424$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $101$ | $19095$ | $2685737$ | $373318339$ | $51888966536$ | $7212547993731$ | $1002544325750159$ | $139353666791843539$ | $19370159743614993263$ | $2692452204311085244950$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 33 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+92x^5+36x^4+99x^3+46x^2+72x+81$
- $y^2=102x^6+98x^5+14x^4+19x^3+116x^2+27x+108$
- $y^2=109x^6+116x^5+132x^4+128x^3+34x^2+111x+126$
- $y^2=134x^6+65x^5+108x^4+27x^3+104x^2+50x+34$
- $y^2=74x^6+39x^5+32x^4+37x^3+15x^2+6x+62$
- $y^2=104x^6+131x^5+87x^4+116x^3+19x^2+84x+93$
- $y^2=129x^6+32x^5+29x^4+6x^3+26x^2+20x+115$
- $y^2=95x^6+8x^5+20x^4+14x^3+115x^2+112x+89$
- $y^2=35x^6+45x^5+125x^4+132x^3+49x^2+92x+83$
- $y^2=72x^6+111x^5+88x^4+34x^3+131x^2+100x+4$
- $y^2=102x^6+26x^5+41x^4+110x^3+8x^2+76x+16$
- $y^2=37x^6+64x^5+36x^4+133x^3+112x^2+98x+3$
- $y^2=85x^6+125x^5+104x^4+37x^3+104x^2+2x+10$
- $y^2=58x^6+11x^5+63x^4+40x^3+71x^2+18x+86$
- $y^2=7x^6+44x^5+41x^4+53x^3+55x^2+121x+85$
- $y^2=77x^6+83x^5+32x^4+38x^3+30x^2+20x+114$
- $y^2=5x^6+55x^5+99x^4+x^3+97x^2+95x+106$
- $y^2=68x^6+115x^5+26x^4+127x^3+77x^2+133x+66$
- $y^2=39x^6+133x^5+56x^4+91x^3+123x^2+90x+101$
- $y^2=97x^6+64x^5+48x^4+122x^3+137x^2+31x+3$
- and 13 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 4.0.248725.1. |
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_yx | $2$ | (not in LMFDB) |