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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 206310.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206310.n1 | 206310ce3 | \([1, 1, 0, -255782, 49675986]\) | \(12501706118329/2570490\) | \(380524772315610\) | \([2]\) | \(1576960\) | \(1.7948\) | |
| 206310.n2 | 206310ce2 | \([1, 1, 0, -17732, 590076]\) | \(4165509529/1368900\) | \(202646328452100\) | \([2, 2]\) | \(788480\) | \(1.4482\) | |
| 206310.n3 | 206310ce1 | \([1, 1, 0, -7152, -228816]\) | \(273359449/9360\) | \(1385615921040\) | \([2]\) | \(394240\) | \(1.1016\) | \(\Gamma_0(N)\)-optimal |
| 206310.n4 | 206310ce4 | \([1, 1, 0, 51038, 4124854]\) | \(99317171591/106616250\) | \(-15783031350596250\) | \([2]\) | \(1576960\) | \(1.7948\) |
Rank
sage: E.rank()
The elliptic curves in class 206310.n have rank \(1\).
Complex multiplication
The elliptic curves in class 206310.n do not have complex multiplication.Modular form 206310.2.a.n
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.
