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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 106722dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.a2 | 106722dy1 | \([1, -1, 0, 132291, -395005451]\) | \(4913/1296\) | \(-67541546572851981168\) | \([2]\) | \(4587520\) | \(2.4841\) | \(\Gamma_0(N)\)-optimal |
106722.a1 | 106722dy2 | \([1, -1, 0, -7338249, -7439724671]\) | \(838561807/26244\) | \(1367716318100252618652\) | \([2]\) | \(9175040\) | \(2.8307\) |
Rank
sage: E.rank()
The elliptic curves in class 106722dy have rank \(0\).
Complex multiplication
The elliptic curves in class 106722dy do not have complex multiplication.Modular form 106722.2.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 Cremona 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 Cremona labels.