Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 40 x + 668 x^{2} - 5560 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0599794008767$, $\pm0.246845953101$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.8505600.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14390$ | $368240100$ | $7211152041110$ | $139357562640051600$ | $2692455826051605959750$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $100$ | $19058$ | $2685100$ | $373311478$ | $51888914500$ | $7212547443458$ | $1002544311085900$ | $139353666420160798$ | $19370159736768400900$ | $2692452204218679358898$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=107x^6+116x^5+72x^4+81x^3+83x^2+93x+70$
- $y^2=85x^6+107x^5+98x^4+30x^3+76x^2+60x+39$
- $y^2=73x^6+89x^5+52x^4+60x^2+120x+116$
- $y^2=7x^6+3x^5+108x^4+88x^3+35x^2+34x+121$
- $y^2=65x^6+81x^5+25x^4+65x^3+22x^2+26x+87$
- $y^2=48x^6+102x^5+42x^4+33x^3+25x^2+123x+60$
- $y^2=134x^6+109x^5+37x^4+112x^3+78x^2+24x+84$
- $y^2=2x^6+47x^5+136x^4+120x^3+132x^2+71x+108$
- $y^2=118x^6+105x^5+121x^4+24x^3+39x^2+100x+37$
- $y^2=33x^6+46x^5+36x^4+8x^3+121x^2+45x+121$
- $y^2=130x^6+26x^5+60x^4+31x^3+54x^2+69x+27$
- $y^2=3x^6+124x^5+25x^4+135x^3+92x^2+129x+56$
- $y^2=19x^6+78x^5+48x^4+3x^3+82x^2+53x+21$
- $y^2=76x^6+4x^5+118x^4+89x^3+92x^2+17x+48$
- $y^2=10x^6+89x^5+56x^4+63x^3+58x^2+117x+134$
- $y^2=23x^6+110x^5+49x^4+62x^2+21x+72$
- $y^2=120x^6+109x^5+10x^4+105x^3+86x^2+85x+109$
- $y^2=116x^6+98x^5+138x^4+x^3+131x^2+30x+95$
- $y^2=136x^6+32x^5+123x^4+101x^3+117x^2+45x+104$
- $y^2=104x^6+122x^5+16x^4+6x^3+13x^2+64x+70$
- $y^2=58x^6+60x^5+50x^4+38x^3+130x^2+126x+7$
- $y^2=102x^6+114x^5+88x^4+86x^3+137x^2+35x+80$
- $y^2=57x^6+117x^5+109x^4+128x^3+12x^2+101x+101$
- $y^2=97x^6+42x^5+123x^4+131x^3+96x^2+32x+33$
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 4.0.8505600.1. |
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.bo_zs | $2$ | (not in LMFDB) |