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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 360672.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360672.bu1 | 360672bu4 | \([0, 1, 0, -1082112, -433628712]\) | \(11339065490696/351\) | \(4337810800128\) | \([2]\) | \(3538944\) | \(1.9293\) | |
| 360672.bu2 | 360672bu2 | \([0, 1, 0, -106737, 1880127]\) | \(1360251712/771147\) | \(76241362623049728\) | \([2]\) | \(3538944\) | \(1.9293\) | |
| 360672.bu3 | 360672bu1 | \([0, 1, 0, -67722, -6773400]\) | \(22235451328/123201\) | \(190321448855616\) | \([2, 2]\) | \(1769472\) | \(1.5828\) | \(\Gamma_0(N)\)-optimal |
| 360672.bu4 | 360672bu3 | \([0, 1, 0, -30152, -14212260]\) | \(-245314376/6908733\) | \(-85381129978919424\) | \([2]\) | \(3538944\) | \(1.9293\) |
Rank
sage: E.rank()
The elliptic curves in class 360672.bu have rank \(2\).
Complex multiplication
The elliptic curves in class 360672.bu do not have complex multiplication.Modular form 360672.2.a.bu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
