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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 141120by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.oo3 | 141120by1 | \([0, 0, 0, -125832, 16466744]\) | \(2508888064/118125\) | \(10374269996160000\) | \([2]\) | \(1179648\) | \(1.8340\) | \(\Gamma_0(N)\)-optimal |
| 141120.oo2 | 141120by2 | \([0, 0, 0, -346332, -57003856]\) | \(3269383504/893025\) | \(1254871698735513600\) | \([2, 2]\) | \(2359296\) | \(2.1805\) | |
| 141120.oo4 | 141120by3 | \([0, 0, 0, 888468, -371630896]\) | \(13799183324/18600435\) | \(-104548739243221647360\) | \([2]\) | \(4718592\) | \(2.5271\) | |
| 141120.oo1 | 141120by4 | \([0, 0, 0, -5109132, -4444495216]\) | \(2624033547076/324135\) | \(1821887799645634560\) | \([2]\) | \(4718592\) | \(2.5271\) |
Rank
sage: E.rank()
The elliptic curves in class 141120by have rank \(1\).
Complex multiplication
The elliptic curves in class 141120by do not have complex multiplication.Modular form 141120.2.a.by
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
