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SageMath
sage: E = EllipticCurve("bb1")
sage: E.isogeny_class()
Elliptic curves in class 303450.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 303450.bb1 | 303450bb6 | [1, 1, 0, -121380150, -514768889250] | [2] | 31457280 | |
| 303450.bb2 | 303450bb4 | [1, 1, 0, -7586400, -8045320500] | [2, 2] | 15728640 | |
| 303450.bb3 | 303450bb5 | [1, 1, 0, -7080650, -9163533750] | [2] | 31457280 | |
| 303450.bb4 | 303450bb3 | [1, 1, 0, -2673400, 1589072500] | [2] | 15728640 | |
| 303450.bb5 | 303450bb2 | [1, 1, 0, -505900, -108080000] | [2, 2] | 7864320 | |
| 303450.bb6 | 303450bb1 | [1, 1, 0, 72100, -10398000] | [2] | 3932160 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.bb have rank \(2\).
Complex multiplication
The elliptic curves in class 303450.bb do not have complex multiplication.Modular form 303450.2.a.bb
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
