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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4080.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4080.n1 | 4080w2 | \([0, -1, 0, -185640, 30848112]\) | \(172735174415217961/39657600\) | \(162437529600\) | \([2]\) | \(16128\) | \(1.5318\) | |
| 4080.n2 | 4080w1 | \([0, -1, 0, -11560, 488560]\) | \(-41713327443241/639221760\) | \(-2618252328960\) | \([2]\) | \(8064\) | \(1.1853\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4080.n have rank \(0\).
Complex multiplication
The elliptic curves in class 4080.n do not have complex multiplication.Modular form 4080.2.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.
