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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 466578cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.cs2 | 466578cs1 | \([1, -1, 0, 695007, -986241803]\) | \(2924207/34776\) | \(-441532230962177003544\) | \([]\) | \(24330240\) | \(2.6423\) | \(\Gamma_0(N)\)-optimal* |
466578.cs1 | 466578cs2 | \([1, -1, 0, -6303663, 27804886843]\) | \(-2181825073/25039686\) | \(-317915471076960836357334\) | \([]\) | \(72990720\) | \(3.1916\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578cs have rank \(0\).
Complex multiplication
The elliptic curves in class 466578cs do not have complex multiplication.Modular form 466578.2.a.cs
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 Cremona 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 Cremona labels.