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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 10800.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10800.bu1 | 10800da3 | \([0, 0, 0, -49275, 5582250]\) | \(-1167051/512\) | \(-5804752896000000\) | \([]\) | \(46656\) | \(1.7320\) | |
| 10800.bu2 | 10800da1 | \([0, 0, 0, -1275, -17750]\) | \(-132651/2\) | \(-3456000000\) | \([]\) | \(5184\) | \(0.63336\) | \(\Gamma_0(N)\)-optimal |
| 10800.bu3 | 10800da2 | \([0, 0, 0, 4725, -87750]\) | \(9261/8\) | \(-10077696000000\) | \([]\) | \(15552\) | \(1.1827\) |
Rank
sage: E.rank()
The elliptic curves in class 10800.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 10800.bu do not have complex multiplication.Modular form 10800.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
