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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 106722do
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.dl2 | 106722do1 | \([1, -1, 0, 1252872, 661702432]\) | \(596183/864\) | \(-315193884006642578784\) | \([]\) | \(4536000\) | \(2.6188\) | \(\Gamma_0(N)\)-optimal |
106722.dl1 | 106722do2 | \([1, -1, 0, -37967463, 90515489917]\) | \(-16591834777/98304\) | \(-35862059691422444519424\) | \([]\) | \(13608000\) | \(3.1681\) |
Rank
sage: E.rank()
The elliptic curves in class 106722do have rank \(0\).
Complex multiplication
The elliptic curves in class 106722do do not have complex multiplication.Modular form 106722.2.a.do
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.