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SageMath
sage: E = EllipticCurve("s1")
sage: E.isogeny_class()
Elliptic curves in class 424830.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
424830.s1 | 424830s2 | [1, 1, 0, -10875981078, -436571405239668] | [] | 349780032 | |
424830.s2 | 424830s1 | [1, 1, 0, -133092453, -609944793093] | [] | 116593344 | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.s have rank \(1\).
Complex multiplication
The elliptic curves in class 424830.s do not have complex multiplication.Modular form 424830.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.