Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 687 x^{2} - 5617 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.0433563628684$, $\pm0.224858212489$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1962053.1 |
Galois group: | $D_{4}$ |
Jacobians: | $7$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13799$ | $346561885$ | $6608588281487$ | $124099189615763525$ | $2329197181830656121904$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $97$ | $18463$ | $2570083$ | $352278939$ | $48261789402$ | $6611855078791$ | $905824257619735$ | $124097929073112051$ | $17001416394560174821$ | $2329194047474836175118$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+47x^5+114x^4+76x^3+87x^2+114x+79$
- $y^2=69x^6+130x^5+89x^4+130x^3+61x^2+36x+22$
- $y^2=27x^6+47x^5+32x^4+111x^3+54x^2+5x+3$
- $y^2=20x^6+105x^5+86x^4+36x^3+28x^2+13x+90$
- $y^2=16x^6+84x^5+12x^4+124x^3+77x^2+129$
- $y^2=75x^6+60x^5+119x^4+51x^3+84x^2+87x+3$
- $y^2=120x^6+62x^5+119x^4+5x^3+61x^2+108x+127$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{137}$.
Endomorphism algebra over $\F_{137}$The endomorphism algebra of this simple isogeny class is 4.0.1962053.1. |
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 |
---|---|---|
2.137.bp_bal | $2$ | (not in LMFDB) |