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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 19600.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.bu1 | 19600cc3 | \([0, 0, 0, -5246675, -4625440750]\) | \(2121328796049/120050\) | \(903920796800000000\) | \([2]\) | \(442368\) | \(2.5098\) | |
| 19600.bu2 | 19600cc4 | \([0, 0, 0, -1718675, 810423250]\) | \(74565301329/5468750\) | \(41177150000000000000\) | \([2]\) | \(442368\) | \(2.5098\) | |
| 19600.bu3 | 19600cc2 | \([0, 0, 0, -346675, -63540750]\) | \(611960049/122500\) | \(922368160000000000\) | \([2, 2]\) | \(221184\) | \(2.1632\) | |
| 19600.bu4 | 19600cc1 | \([0, 0, 0, 45325, -5916750]\) | \(1367631/2800\) | \(-21082700800000000\) | \([2]\) | \(110592\) | \(1.8167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.bu do not have complex multiplication.Modular form 19600.2.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.
