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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2550.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2550.d1 | 2550a3 | \([1, 1, 0, -4650, -123750]\) | \(711882749089/1721250\) | \(26894531250\) | \([2]\) | \(3072\) | \(0.88009\) | |
| 2550.d2 | 2550a4 | \([1, 1, 0, -4150, 100750]\) | \(506071034209/2505630\) | \(39150468750\) | \([2]\) | \(3072\) | \(0.88009\) | |
| 2550.d3 | 2550a2 | \([1, 1, 0, -400, -500]\) | \(454756609/260100\) | \(4064062500\) | \([2, 2]\) | \(1536\) | \(0.53352\) | |
| 2550.d4 | 2550a1 | \([1, 1, 0, 100, 0]\) | \(6967871/4080\) | \(-63750000\) | \([2]\) | \(768\) | \(0.18695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2550.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2550.d do not have complex multiplication.Modular form 2550.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
