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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 299832o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299832.o1 | 299832o1 | \([0, 1, 0, -3203, 30930]\) | \(256000/117\) | \(1661406890832\) | \([2]\) | \(460800\) | \(1.0398\) | \(\Gamma_0(N)\)-optimal |
299832.o2 | 299832o2 | \([0, 1, 0, 11212, 244272]\) | \(686000/507\) | \(-115190877764352\) | \([2]\) | \(921600\) | \(1.3864\) |
Rank
sage: E.rank()
The elliptic curves in class 299832o have rank \(0\).
Complex multiplication
The elliptic curves in class 299832o do not have complex multiplication.Modular form 299832.2.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 Cremona 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 Cremona labels.