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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 26010bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26010.br3 | 26010bd1 | \([1, -1, 1, -2222, 46461]\) | \(-1860867/320\) | \(-208548596160\) | \([2]\) | \(36864\) | \(0.89824\) | \(\Gamma_0(N)\)-optimal |
| 26010.br2 | 26010bd2 | \([1, -1, 1, -36902, 2737629]\) | \(8527173507/200\) | \(130342872600\) | \([2]\) | \(73728\) | \(1.2448\) | |
| 26010.br4 | 26010bd3 | \([1, -1, 1, 15118, -198611]\) | \(804357/500\) | \(-237549885313500\) | \([2]\) | \(110592\) | \(1.4476\) | |
| 26010.br1 | 26010bd4 | \([1, -1, 1, -62912, -1571939]\) | \(57960603/31250\) | \(14846867832093750\) | \([2]\) | \(221184\) | \(1.7941\) |
Rank
sage: E.rank()
The elliptic curves in class 26010bd have rank \(1\).
Complex multiplication
The elliptic curves in class 26010bd do not have complex multiplication.Modular form 26010.2.a.bd
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.
