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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 397800.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.dy1 | 397800dy3 | \([0, 0, 0, -6622275, 6559240750]\) | \(2753580869496292/39328497\) | \(458727589008000000\) | \([2]\) | \(10485760\) | \(2.5284\) | |
397800.dy2 | 397800dy2 | \([0, 0, 0, -425775, 96291250]\) | \(2927363579728/320445801\) | \(934419955716000000\) | \([2, 2]\) | \(5242880\) | \(2.1818\) | |
397800.dy3 | 397800dy1 | \([0, 0, 0, -100650, -10674875]\) | \(618724784128/87947613\) | \(16028452469250000\) | \([2]\) | \(2621440\) | \(1.8352\) | \(\Gamma_0(N)\)-optimal |
397800.dy4 | 397800dy4 | \([0, 0, 0, 568725, 479173750]\) | \(1744147297148/9513325341\) | \(-110963426777424000000\) | \([2]\) | \(10485760\) | \(2.5284\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.dy do not have complex multiplication.Modular form 397800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.