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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 89280.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.dy1 | 89280cq2 | \([0, 0, 0, -300972, 63565616]\) | \(-15777367606441/3574920\) | \(-683177850961920\) | \([]\) | \(552960\) | \(1.8386\) | |
| 89280.dy2 | 89280cq1 | \([0, 0, 0, 1428, 303536]\) | \(1685159/209250\) | \(-39988297728000\) | \([]\) | \(184320\) | \(1.2893\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89280.dy have rank \(2\).
Complex multiplication
The elliptic curves in class 89280.dy do not have complex multiplication.Modular form 89280.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
