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SageMath
E = EllipticCurve("nx1")
E.isogeny_class()
Elliptic curves in class 381150.nx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.nx1 | 381150nx2 | \([1, -1, 1, -4415555, -3568029803]\) | \(139798359/98\) | \(6674266105417968750\) | \([2]\) | \(12441600\) | \(2.5484\) | |
| 381150.nx2 | 381150nx1 | \([1, -1, 1, -331805, -31502303]\) | \(59319/28\) | \(1906933172976562500\) | \([2]\) | \(6220800\) | \(2.2018\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.nx have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.nx do not have complex multiplication.Modular form 381150.2.a.nx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
