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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 38640bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bb2 | 38640bu1 | \([0, -1, 0, -3080, 65520]\) | \(789145184521/17996580\) | \(73713991680\) | \([2]\) | \(46080\) | \(0.87189\) | \(\Gamma_0(N)\)-optimal |
| 38640.bb1 | 38640bu2 | \([0, -1, 0, -6760, -117008]\) | \(8341959848041/3327411150\) | \(13629076070400\) | \([2]\) | \(92160\) | \(1.2185\) |
Rank
sage: E.rank()
The elliptic curves in class 38640bu have rank \(1\).
Complex multiplication
The elliptic curves in class 38640bu do not have complex multiplication.Modular form 38640.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
