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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 422370.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.n1 | 422370n2 | \([1, -1, 0, -34171425, -75587012325]\) | \(128666016371695321/2476965634650\) | \(84951121226359531577850\) | \([2]\) | \(53084160\) | \(3.1926\) | \(\Gamma_0(N)\)-optimal* |
422370.n2 | 422370n1 | \([1, -1, 0, 40545, -3475021959]\) | \(214921799/152106418620\) | \(-5216709762435141376380\) | \([2]\) | \(26542080\) | \(2.8461\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422370.n have rank \(0\).
Complex multiplication
The elliptic curves in class 422370.n do not have complex multiplication.Modular form 422370.2.a.n
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.