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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8550.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.o1 | 8550j2 | \([1, -1, 0, -89442, -10259784]\) | \(6947097508441/10687500\) | \(121737304687500\) | \([2]\) | \(36864\) | \(1.6021\) | |
8550.o2 | 8550j1 | \([1, -1, 0, -3942, -256284]\) | \(-594823321/2166000\) | \(-24672093750000\) | \([2]\) | \(18432\) | \(1.2555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.o have rank \(1\).
Complex multiplication
The elliptic curves in class 8550.o do not have complex multiplication.Modular form 8550.2.a.o
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.