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SageMath
sage: E = EllipticCurve("dx1")
sage: E.isogeny_class()
Elliptic curves in class 205350.dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 205350.dx1 | 205350v3 | [1, 0, 0, -11670896838, 485292507728292] | [2] | 226934784 | |
| 205350.dx2 | 205350v6 | [1, 0, 0, -10374453838, -404953052500708] | [2] | 453869568 | |
| 205350.dx3 | 205350v4 | [1, 0, 0, -1003648838, 1374423104292] | [2, 2] | 226934784 | |
| 205350.dx4 | 205350v2 | [1, 0, 0, -729848838, 7573528904292] | [2, 2] | 113467392 | |
| 205350.dx5 | 205350v1 | [1, 0, 0, -28920838, 206074696292] | [2] | 56733696 | \(\Gamma_0(N)\)-optimal |
| 205350.dx6 | 205350v5 | [1, 0, 0, 3986356162, 10960222709292] | [2] | 453869568 |
Rank
sage: E.rank()
The elliptic curves in class 205350.dx have rank \(1\).
Complex multiplication
The elliptic curves in class 205350.dx do not have complex multiplication.Modular form 205350.2.a.dx
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
