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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 28050.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28050.cy1 | 28050do4 | \([1, 0, 0, -12098488, 16196019092]\) | \(12534210458299016895673/315581882565708\) | \(4930966915089187500\) | \([2]\) | \(1966080\) | \(2.6950\) | |
| 28050.cy2 | 28050do2 | \([1, 0, 0, -784988, 232670592]\) | \(3423676911662954233/483711578981136\) | \(7557993421580250000\) | \([2, 2]\) | \(983040\) | \(2.3484\) | |
| 28050.cy3 | 28050do1 | \([1, 0, 0, -206988, -32631408]\) | \(62768149033310713/6915442583808\) | \(108053790372000000\) | \([2]\) | \(491520\) | \(2.0018\) | \(\Gamma_0(N)\)-optimal |
| 28050.cy4 | 28050do3 | \([1, 0, 0, 1280512, 1250962092]\) | \(14861225463775641287/51859390496937804\) | \(-810302976514653187500\) | \([2]\) | \(1966080\) | \(2.6950\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.cy have rank \(1\).
Complex multiplication
The elliptic curves in class 28050.cy do not have complex multiplication.Modular form 28050.2.a.cy
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.
