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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 | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
97461.w1 | 97461w2 | [1, -1, 0, -5167500, 4522649543] | [2] | 2764800 | |
97461.w2 | 97461w1 | [1, -1, 0, -323115, 70659728] | [2] | 1382400 | \(\Gamma_0(N)\)-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.