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SageMath
sage: E = EllipticCurve("14400.dz1")
sage: E.isogeny_class()
Elliptic curves in class 14400dw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 14400.dz3 | 14400dw1 | [0, 0, 0, -1200, 11000] | [2] | 9216 | \(\Gamma_0(N)\)-optimal |
| 14400.dz4 | 14400dw2 | [0, 0, 0, 3300, 74000] | [2] | 18432 | |
| 14400.dz1 | 14400dw3 | [0, 0, 0, -37200, -2761000] | [2] | 27648 | |
| 14400.dz2 | 14400dw4 | [0, 0, 0, -32700, -3454000] | [2] | 55296 |
Rank
sage: E.rank()
The elliptic curves in class 14400dw have rank \(1\).
Modular form 14400.2.a.dz
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.
