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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 14490y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.be4 | 14490y1 | \([1, -1, 0, -16569, -813267]\) | \(690080604747409/3406760000\) | \(2483528040000\) | \([2]\) | \(59904\) | \(1.2261\) | \(\Gamma_0(N)\)-optimal |
| 14490.be3 | 14490y2 | \([1, -1, 0, -25569, 174933]\) | \(2535986675931409/1450751712200\) | \(1057597998193800\) | \([2]\) | \(119808\) | \(1.5726\) | |
| 14490.be2 | 14490y3 | \([1, -1, 0, -95229, 10744785]\) | \(131010595463836369/7704101562500\) | \(5616290039062500\) | \([6]\) | \(179712\) | \(1.7754\) | |
| 14490.be1 | 14490y4 | \([1, -1, 0, -1501479, 708526035]\) | \(513516182162686336369/1944885031250\) | \(1417821187781250\) | \([6]\) | \(359424\) | \(2.1219\) |
Rank
sage: E.rank()
The elliptic curves in class 14490y have rank \(0\).
Complex multiplication
The elliptic curves in class 14490y do not have complex multiplication.Modular form 14490.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
