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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 203280.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.dy1 | 203280bu3 | \([0, 1, 0, -63870616, 196447891220]\) | \(3971101377248209009/56495958750\) | \(409952408285629440000\) | \([2]\) | \(17694720\) | \(3.0949\) | |
| 203280.dy2 | 203280bu2 | \([0, 1, 0, -4106296, 2883211604]\) | \(1055257664218129/115307784900\) | \(836709477274537574400\) | \([2, 2]\) | \(8847360\) | \(2.7483\) | |
| 203280.dy3 | 203280bu1 | \([0, 1, 0, -969976, -319598380]\) | \(13908844989649/1980372240\) | \(14370202525149757440\) | \([2]\) | \(4423680\) | \(2.4017\) | \(\Gamma_0(N)\)-optimal |
| 203280.dy4 | 203280bu4 | \([0, 1, 0, 5476904, 14348552084]\) | \(2503876820718671/13702874328990\) | \(-99432356860476839485440\) | \([2]\) | \(17694720\) | \(3.0949\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.dy do not have complex multiplication.Modular form 203280.2.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 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.
