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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 7350cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.co1 | 7350cw1 | \([1, 0, 0, -208888, -36566608]\) | \(4386781853/27216\) | \(6253779656250000\) | \([2]\) | \(76800\) | \(1.8690\) | \(\Gamma_0(N)\)-optimal |
7350.co2 | 7350cw2 | \([1, 0, 0, -86388, -79074108]\) | \(-310288733/11573604\) | \(-2659419798820312500\) | \([2]\) | \(153600\) | \(2.2156\) |
Rank
sage: E.rank()
The elliptic curves in class 7350cw have rank \(1\).
Complex multiplication
The elliptic curves in class 7350cw do not have complex multiplication.Modular form 7350.2.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 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.