Invariants
Base field: | $\F_{137}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 686 x^{2} - 5617 x^{3} + 18769 x^{4}$ |
Frobenius angles: | $\pm0.0179276178433$, $\pm0.228596896516$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.448668.1 |
Galois group: | $D_{4}$ |
Jacobians: | $2$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $13798$ | $346522972$ | $6608271338296$ | $124097788085696704$ | $2329192779126488895478$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $97$ | $18461$ | $2569960$ | $352274961$ | $48261698177$ | $6611853417698$ | $905824232124377$ | $124097928728392609$ | $17001416390249622232$ | $2329194047421656116541$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=54x^6+53x^5+65x^4+79x^3+126x^2+33x+109$
- $y^2=48x^6+23x^5+24x^4+51x^3+20x+127$
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 4.0.448668.1. |
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_bak | $2$ | (not in LMFDB) |