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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 14490.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.u1 | 14490s1 | \([1, -1, 0, -9703989, -11632766027]\) | \(138626767243242683688529/5300196249600\) | \(3863843065958400\) | \([2]\) | \(368640\) | \(2.4821\) | \(\Gamma_0(N)\)-optimal |
| 14490.u2 | 14490s2 | \([1, -1, 0, -9689589, -11669022347]\) | \(-138010547060620856386129/857302254769101120\) | \(-624973343726674716480\) | \([2]\) | \(737280\) | \(2.8287\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.u have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.u do not have complex multiplication.Modular form 14490.2.a.u
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.
