Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 39 x + 639 x^{2} - 5343 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.00608336417129$, $\pm0.267928225148$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.226981.1 |
Galois group: | $C_4$ |
Jacobians: | $1$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14027$ | $347743357$ | $6610348772651$ | $124097633743721989$ | $2329183175938050519152$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $99$ | $18527$ | $2570769$ | $352274523$ | $48261499194$ | $6611849436647$ | $905824191029661$ | $124097928637117171$ | $17001416395180327743$ | $2329194047520161837582$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=106x^6+61x^5+77x^4+118x^3+136x^2+23x+107$
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 4.0.226981.1. |
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.bn_yp | $2$ | (not in LMFDB) |