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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 350900.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350900.y1 | 350900y1 | \([0, -1, 0, -2649904033, -52503230158938]\) | \(4646415367355940880384/38478378125\) | \(17041698507375781250000\) | \([2]\) | \(135475200\) | \(3.8536\) | \(\Gamma_0(N)\)-optimal |
| 350900.y2 | 350900y2 | \([0, -1, 0, -2648073908, -52579374339688]\) | \(-289799689905740628304/835751962890625\) | \(-5922342332521914062500000000\) | \([2]\) | \(270950400\) | \(4.2002\) |
Rank
sage: E.rank()
The elliptic curves in class 350900.y have rank \(1\).
Complex multiplication
The elliptic curves in class 350900.y do not have complex multiplication.Modular form 350900.2.a.y
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.
