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SageMath
E = EllipticCurve("kq1")
E.isogeny_class()
Elliptic curves in class 286650.kq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.kq1 | 286650kq1 | \([1, -1, 1, -25955, -2468203]\) | \(-38958219/30758\) | \(-1526617100531250\) | \([]\) | \(1492992\) | \(1.6120\) | \(\Gamma_0(N)\)-optimal |
| 286650.kq2 | 286650kq2 | \([1, -1, 1, 212920, 39414547]\) | \(29503629/35672\) | \(-1290705075694125000\) | \([]\) | \(4478976\) | \(2.1613\) |
Rank
sage: E.rank()
The elliptic curves in class 286650.kq have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.kq do not have complex multiplication.Modular form 286650.2.a.kq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
