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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 286110dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.dy4 | 286110dy1 | \([1, -1, 1, -48712883, -130849752369]\) | \(726497538898787209/1038579300\) | \(18275140266961119300\) | \([2]\) | \(26542080\) | \(2.9673\) | \(\Gamma_0(N)\)-optimal |
| 286110.dy3 | 286110dy2 | \([1, -1, 1, -49155053, -128352906813]\) | \(746461053445307689/27443694341250\) | \(482907143951310106091250\) | \([2]\) | \(53084160\) | \(3.3139\) | |
| 286110.dy2 | 286110dy3 | \([1, -1, 1, -62016998, -53762963403]\) | \(1499114720492202169/796539777000000\) | \(14016143161036360377000000\) | \([2]\) | \(79626240\) | \(3.5166\) | |
| 286110.dy1 | 286110dy4 | \([1, -1, 1, -573165518, 5241326784981]\) | \(1183430669265454849849/10449720703125000\) | \(183876292932255580078125000\) | \([2]\) | \(159252480\) | \(3.8632\) |
Rank
sage: E.rank()
The elliptic curves in class 286110dy have rank \(0\).
Complex multiplication
The elliptic curves in class 286110dy do not have complex multiplication.Modular form 286110.2.a.dy
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
