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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 425880.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.dy1 | 425880dy2 | \([0, 0, 0, -15046259787, -710093280265434]\) | \(1936101054887046531846/905403781953125\) | \(176166636628379239795680000000\) | \([2]\) | \(671956992\) | \(4.5678\) | \(\Gamma_0(N)\)-optimal* |
425880.dy2 | 425880dy1 | \([0, 0, 0, -786884787, -14837525890434]\) | \(-553867390580563692/657061767578125\) | \(-63923060604869943750000000000\) | \([2]\) | \(335978496\) | \(4.2212\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 425880.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 425880.dy do not have complex multiplication.Modular form 425880.2.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.