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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2040.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2040.n1 | 2040o2 | \([0, 1, 0, -720, 7200]\) | \(20183398562/3825\) | \(7833600\) | \([2]\) | \(640\) | \(0.32405\) | |
| 2040.n2 | 2040o1 | \([0, 1, 0, -40, 128]\) | \(-7086244/4335\) | \(-4439040\) | \([2]\) | \(320\) | \(-0.022526\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2040.n have rank \(0\).
Complex multiplication
The elliptic curves in class 2040.n do not have complex multiplication.Modular form 2040.2.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.
