Show commands:
SageMath
E = EllipticCurve("gy1")
E.isogeny_class()
Elliptic curves in class 381150.gy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.gy1 | 381150gy3 | \([1, -1, 0, -1271067, 483642341]\) | \(416832723/56000\) | \(30510930767625000000\) | \([2]\) | \(9953280\) | \(2.4662\) | |
| 381150.gy2 | 381150gy1 | \([1, -1, 0, -318192, -68919284]\) | \(4767078987/6860\) | \(5127008256562500\) | \([2]\) | \(3317760\) | \(1.9169\) | \(\Gamma_0(N)\)-optimal |
| 381150.gy3 | 381150gy2 | \([1, -1, 0, -227442, -109121534]\) | \(-1740992427/5882450\) | \(-4396409580002343750\) | \([2]\) | \(6635520\) | \(2.2634\) | |
| 381150.gy4 | 381150gy4 | \([1, -1, 0, 1995933, 2558187341]\) | \(1613964717/6125000\) | \(-3337133052708984375000\) | \([2]\) | \(19906560\) | \(2.8128\) |
Rank
sage: E.rank()
The elliptic curves in class 381150.gy have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.gy do not have complex multiplication.Modular form 381150.2.a.gy
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
