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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 474075cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474075.cq2 | 474075cq1 | \([1, -1, 0, -95706417, 360361275616]\) | \(1953326569433829507/262451171875\) | \(13026284122467041015625\) | \([2]\) | \(61931520\) | \(3.2623\) | \(\Gamma_0(N)\)-optimal* |
474075.cq1 | 474075cq2 | \([1, -1, 0, -1531253292, 23063535103741]\) | \(8000051600110940079507/144453125\) | \(7169666781005859375\) | \([2]\) | \(123863040\) | \(3.6089\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474075cq have rank \(1\).
Complex multiplication
The elliptic curves in class 474075cq do not have complex multiplication.Modular form 474075.2.a.cq
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.