Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 649 x^{2} - 5421 x^{3} + 19321 x^{4}$ |
Frobenius angles: | $\pm0.0948109279217$, $\pm0.254073133352$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.18690957.1 |
Galois group: | $D_{4}$ |
Jacobians: | $32$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14511$ | $369029241$ | $7213492497897$ | $139362731528628573$ | $2692465892359233591216$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $101$ | $19099$ | $2685971$ | $373325323$ | $51889108496$ | $7212550154191$ | $1002544350971537$ | $139353667010804899$ | $19370159744840214923$ | $2692452204312585489814$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+2x^5+30x^4+92x^3+35x^2+39x+137$
- $y^2=70x^6+90x^5+5x^4+122x^3+97x^2+70x+52$
- $y^2=102x^6+67x^5+117x^4+32x^3+79x^2+63x+123$
- $y^2=70x^6+58x^5+31x^4+115x^3+80x^2+29x+8$
- $y^2=73x^6+31x^5+83x^4+13x^3+86x^2+132x+102$
- $y^2=14x^6+18x^5+107x^4+36x^3+12x^2+15x+40$
- $y^2=125x^6+76x^5+20x^4+54x^3+36x^2+88x+6$
- $y^2=135x^6+91x^5+98x^4+30x^3+19x^2+60x+76$
- $y^2=78x^6+98x^5+99x^4+122x^3+55x^2+58x+39$
- $y^2=95x^6+39x^5+100x^4+62x^3+12x^2+122x+66$
- $y^2=5x^6+54x^5+54x^4+93x^3+113x^2+78x+68$
- $y^2=114x^6+99x^5+16x^4+70x^3+101x^2+128x+98$
- $y^2=36x^6+22x^5+70x^4+122x^3+136x^2+134x+54$
- $y^2=16x^6+84x^5+84x^4+59x^3+132x^2+42x+109$
- $y^2=125x^6+130x^5+66x^4+118x^3+122x^2+73x+37$
- $y^2=72x^6+61x^5+111x^4+73x^3+x^2+99x+110$
- $y^2=56x^6+129x^5+42x^4+108x^3+44x^2+51x+104$
- $y^2=68x^6+3x^5+85x^4+138x^3+17x^2+24x+123$
- $y^2=3x^6+122x^5+54x^4+94x^3+48x+32$
- $y^2=108x^6+41x^5+29x^4+107x^3+55x^2+14x+60$
- and 12 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 4.0.18690957.1. |
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_yz | $2$ | (not in LMFDB) |