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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 107712.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.dy1 | 107712dk2 | \([0, 0, 0, -638269644, 4424264927120]\) | \(150476552140919246594353/42832838728685592576\) | \(8185482951579873309597106176\) | \([2]\) | \(49840128\) | \(4.0627\) | |
| 107712.dy2 | 107712dk1 | \([0, 0, 0, -237189324, -1351452113008]\) | \(7722211175253055152433/340131399900069888\) | \(65000122751949458204786688\) | \([2]\) | \(24920064\) | \(3.7161\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107712.dy have rank \(1\).
Complex multiplication
The elliptic curves in class 107712.dy do not have complex multiplication.Modular form 107712.2.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.
