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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 7650.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7650.bw1 | 7650cb4 | \([1, -1, 1, -41855, 3299397]\) | \(711882749089/1721250\) | \(19606113281250\) | \([2]\) | \(24576\) | \(1.4294\) | |
| 7650.bw2 | 7650cb3 | \([1, -1, 1, -37355, -2757603]\) | \(506071034209/2505630\) | \(28540691718750\) | \([2]\) | \(24576\) | \(1.4294\) | |
| 7650.bw3 | 7650cb2 | \([1, -1, 1, -3605, 9897]\) | \(454756609/260100\) | \(2962701562500\) | \([2, 2]\) | \(12288\) | \(1.0828\) | |
| 7650.bw4 | 7650cb1 | \([1, -1, 1, 895, 897]\) | \(6967871/4080\) | \(-46473750000\) | \([4]\) | \(6144\) | \(0.73625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7650.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 7650.bw do not have complex multiplication.Modular form 7650.2.a.bw
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
