Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 593 x^{2} - 4173 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0262161664451$, $\pm0.151730065574$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.6525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $2$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $7831$ | $127292905$ | $1497723535489$ | $17180011184046525$ | $196714503393257094256$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $69$ | $11115$ | $1222587$ | $131065483$ | $14025472224$ | $1500730548495$ | $160578151263417$ | $17181861796228963$ | $1838459211531366699$ | $196715135708369716950$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=58x^6+44x^5+30x^4+22x^3+43x+61$
- $y^2=5x^6+35x^5+105x^4+61x^3+89x^2+75x+36$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$The endomorphism algebra of this simple isogeny class is 4.0.6525.1. |
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 |
---|---|---|
2.107.bn_wv | $2$ | (not in LMFDB) |