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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 6336.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6336.bu1 | 6336bx3 | \([0, 0, 0, -281532, -57496282]\) | \(-52893159101157376/11\) | \(-513216\) | \([]\) | \(12000\) | \(1.3926\) | |
| 6336.bu2 | 6336bx2 | \([0, 0, 0, -372, -5002]\) | \(-122023936/161051\) | \(-7513995456\) | \([]\) | \(2400\) | \(0.58787\) | |
| 6336.bu3 | 6336bx1 | \([0, 0, 0, -12, 38]\) | \(-4096/11\) | \(-513216\) | \([]\) | \(480\) | \(-0.21685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6336.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 6336.bu do not have complex multiplication.Modular form 6336.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
