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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 206910.eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206910.eo1 | 206910q4 | \([1, -1, 1, -676292, -213586491]\) | \(26487576322129/44531250\) | \(57510682994531250\) | \([2]\) | \(2621440\) | \(2.1112\) | |
| 206910.eo2 | 206910q2 | \([1, -1, 1, -55562, -1048539]\) | \(14688124849/8122500\) | \(10489948578202500\) | \([2, 2]\) | \(1310720\) | \(1.7646\) | |
| 206910.eo3 | 206910q1 | \([1, -1, 1, -33782, 2383989]\) | \(3301293169/22800\) | \(29445469693200\) | \([2]\) | \(655360\) | \(1.4180\) | \(\Gamma_0(N)\)-optimal |
| 206910.eo4 | 206910q3 | \([1, -1, 1, 216688, -8453739]\) | \(871257511151/527800050\) | \(-681636858611598450\) | \([2]\) | \(2621440\) | \(2.1112\) |
Rank
sage: E.rank()
The elliptic curves in class 206910.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 206910.eo do not have complex multiplication.Modular form 206910.2.a.eo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
