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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 235200.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.dy1 | 235200dy1 | \([0, -1, 0, -534753, 149883777]\) | \(4386781853/27216\) | \(104921012109312000\) | \([2]\) | \(2949120\) | \(2.1040\) | \(\Gamma_0(N)\)-optimal |
| 235200.dy2 | 235200dy2 | \([0, -1, 0, -221153, 323931777]\) | \(-310288733/11573604\) | \(-44617660399484928000\) | \([2]\) | \(5898240\) | \(2.4506\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.dy do not have complex multiplication.Modular form 235200.2.a.dy
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
