Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 40 x + 670 x^{2} - 5560 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0805640498865$, $\pm0.240340054639$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.145664.2 |
Galois group: | $D_{4}$ |
Jacobians: | $70$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14392$ | $368320064$ | $7211797824952$ | $139360343288800256$ | $2692464149062492728952$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $100$ | $19062$ | $2685340$ | $373318926$ | $51889074900$ | $7212550105542$ | $1002544346735500$ | $139353666814409118$ | $19370159740469887300$ | $2692452204250953137302$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 70 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=18x^6+46x^5+71x^4+88x^3+106x^2+29x+74$
- $y^2=21x^6+111x^5+45x^4+87x^3+12x^2+68x+61$
- $y^2=87x^6+42x^5+11x^4+69x^3+26x^2+7x+24$
- $y^2=124x^6+87x^5+62x^4+99x^3+77x^2+102x+138$
- $y^2=48x^6+12x^5+92x^4+99x^3+132x^2+137x+10$
- $y^2=93x^6+31x^5+64x^4+18x^3+54x^2+25x+85$
- $y^2=130x^6+86x^5+18x^4+107x^3+3x^2+37x+90$
- $y^2=59x^6+118x^5+104x^4+32x^3+77x^2+6x+8$
- $y^2=81x^6+71x^5+46x^4+114x^3+9x^2+46x+97$
- $y^2=4x^6+71x^5+65x^4+10x^3+43x^2+50x+69$
- $y^2=119x^6+64x^5+111x^4+49x^3+121x^2+42x+97$
- $y^2=93x^6+107x^5+71x^4+67x^3+30x^2+82x+59$
- $y^2=92x^6+86x^5+108x^4+97x^3+103x^2+11x+106$
- $y^2=59x^6+10x^5+63x^4+49x^3+114x^2+122x+33$
- $y^2=120x^6+83x^5+120x^4+90x^3+4x^2+116x+93$
- $y^2=29x^6+114x^5+51x^4+48x^3+120x^2+120x+127$
- $y^2=36x^6+25x^5+65x^4+128x^3+14x^2+78x+48$
- $y^2=8x^6+104x^5+131x^4+29x^3+13x^2+70x+128$
- $y^2=133x^6+96x^5+41x^4+78x^3+32x^2+x+103$
- $y^2=39x^6+32x^5+11x^4+42x^3+134x^2+38x+27$
- and 50 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 4.0.145664.2. |
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.bo_zu | $2$ | (not in LMFDB) |