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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5040.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.n1 | 5040x1 | \([0, 0, 0, -737883, 243438858]\) | \(551105805571803/1376829440\) | \(111002148321361920\) | \([2]\) | \(80640\) | \(2.1481\) | \(\Gamma_0(N)\)-optimal |
5040.n2 | 5040x2 | \([0, 0, 0, -461403, 428072202]\) | \(-134745327251163/903920796800\) | \(-72875511985825382400\) | \([2]\) | \(161280\) | \(2.4946\) |
Rank
sage: E.rank()
The elliptic curves in class 5040.n have rank \(1\).
Complex multiplication
The elliptic curves in class 5040.n do not have complex multiplication.Modular form 5040.2.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.