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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 58950bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58950.bl2 | 58950bu1 | \([1, -1, 1, -480380, -121686753]\) | \(1076291879750641/60150618144\) | \(685153134796500000\) | \([]\) | \(940800\) | \(2.1774\) | \(\Gamma_0(N)\)-optimal |
| 58950.bl1 | 58950bu2 | \([1, -1, 1, -51085130, 140549312247]\) | \(1294373635812597347281/2083292441154\) | \(23730002962519781250\) | \([]\) | \(4704000\) | \(2.9821\) |
Rank
sage: E.rank()
The elliptic curves in class 58950bu have rank \(1\).
Complex multiplication
The elliptic curves in class 58950bu do not have complex multiplication.Modular form 58950.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
