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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 660.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 660.d1 | 660d4 | \([0, 1, 0, -249996, -48194796]\) | \(6749703004355978704/5671875\) | \(1452000000\) | \([2]\) | \(1728\) | \(1.4936\) | |
| 660.d2 | 660d3 | \([0, 1, 0, -15621, -757296]\) | \(-26348629355659264/24169921875\) | \(-386718750000\) | \([2]\) | \(864\) | \(1.1470\) | |
| 660.d3 | 660d2 | \([0, 1, 0, -3156, -63900]\) | \(13584145739344/1195803675\) | \(306125740800\) | \([6]\) | \(576\) | \(0.94425\) | |
| 660.d4 | 660d1 | \([0, 1, 0, 219, -4500]\) | \(72268906496/606436875\) | \(-9702990000\) | \([6]\) | \(288\) | \(0.59767\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 660.d have rank \(0\).
Complex multiplication
The elliptic curves in class 660.d do not have complex multiplication.Modular form 660.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
