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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6270.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6270.n1 | 6270n1 | \([1, 1, 1, -3675, -45783]\) | \(5489125095409201/2330634240000\) | \(2330634240000\) | \([2]\) | \(16128\) | \(1.0698\) | \(\Gamma_0(N)\)-optimal |
| 6270.n2 | 6270n2 | \([1, 1, 1, 12325, -320983]\) | \(207053365326094799/165767088643200\) | \(-165767088643200\) | \([2]\) | \(32256\) | \(1.4164\) |
Rank
sage: E.rank()
The elliptic curves in class 6270.n have rank \(1\).
Complex multiplication
The elliptic curves in class 6270.n do not have complex multiplication.Modular form 6270.2.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.
