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SageMath
sage: E = EllipticCurve("w1")
sage: E.isogeny_class()
Elliptic curves in class 97461.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97461.w1 | 97461w2 | \([1, -1, 0, -5167500, 4522649543]\) | \(177930109857804849/634933\) | \(54455740504893\) | \([2]\) | \(2764800\) | \(2.2774\) | |
| 97461.w2 | 97461w1 | \([1, -1, 0, -323115, 70659728]\) | \(43499078731809/82055753\) | \(7037603640544113\) | \([2]\) | \(1382400\) | \(1.9309\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97461.w have rank \(1\).
Complex multiplication
The elliptic curves in class 97461.w do not have complex multiplication.Modular form 97461.2.a.w
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.
