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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 485520.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.cw1 | 485520cw2 | \([0, -1, 0, -174248600, 884280361200]\) | \(5918043195362419129/8515734343200\) | \(841929217206926052556800\) | \([2]\) | \(106168320\) | \(3.4933\) | \(\Gamma_0(N)\)-optimal* |
485520.cw2 | 485520cw1 | \([0, -1, 0, -7784600, 21863670000]\) | \(-527690404915129/1782829440000\) | \(-176263858680755650560000\) | \([2]\) | \(53084160\) | \(3.1467\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.cw have rank \(1\).
Complex multiplication
The elliptic curves in class 485520.cw do not have complex multiplication.Modular form 485520.2.a.cw
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.