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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 417450f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.f2 | 417450f1 | \([1, 1, 0, -562954075, -5141347947875]\) | \(77896100960425/79488\) | \(20133925846526250000000\) | \([]\) | \(155675520\) | \(3.5709\) | \(\Gamma_0(N)\)-optimal* |
417450.f1 | 417450f2 | \([1, 1, 0, -700213450, -2445436563500]\) | \(149895351206425/76548145152\) | \(19389274836195348480000000000\) | \([]\) | \(467026560\) | \(4.1202\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417450f have rank \(1\).
Complex multiplication
The elliptic curves in class 417450f do not have complex multiplication.Modular form 417450.2.a.f
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.