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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 98736.dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.dl1 | 98736db4 | \([0, 1, 0, -3750072, -2591842860]\) | \(803760366578833/65593817586\) | \(475969327417228271616\) | \([2]\) | \(4423680\) | \(2.7104\) | |
| 98736.dl2 | 98736db2 | \([0, 1, 0, -787992, 222133140]\) | \(7457162887153/1370924676\) | \(9947859721991110656\) | \([2, 2]\) | \(2211840\) | \(2.3638\) | |
| 98736.dl3 | 98736db1 | \([0, 1, 0, -749272, 249376532]\) | \(6411014266033/296208\) | \(2149378214658048\) | \([2]\) | \(1105920\) | \(2.0172\) | \(\Gamma_0(N)\)-optimal |
| 98736.dl4 | 98736db3 | \([0, 1, 0, 1554568, 1293151572]\) | \(57258048889007/132611470002\) | \(-962270447240040947712\) | \([2]\) | \(4423680\) | \(2.7104\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.dl have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.dl do not have complex multiplication.Modular form 98736.2.a.dl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
