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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 350727k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350727.k2 | 350727k1 | \([1, 1, 0, -138873, 19843560]\) | \(2000852317801/2094417\) | \(310048882531713\) | \([2]\) | \(3649536\) | \(1.6979\) | \(\Gamma_0(N)\)-optimal |
350727.k1 | 350727k2 | \([1, 1, 0, -173258, 9218595]\) | \(3885442650361/1996623837\) | \(295571984708886093\) | \([2]\) | \(7299072\) | \(2.0445\) |
Rank
sage: E.rank()
The elliptic curves in class 350727k have rank \(0\).
Complex multiplication
The elliptic curves in class 350727k do not have complex multiplication.Modular form 350727.2.a.k
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.