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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 7350bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7350.bo3 | 7350bu1 | \([1, 1, 1, -4313, 67031]\) | \(4826809/1680\) | \(3088286250000\) | \([4]\) | \(18432\) | \(1.0981\) | \(\Gamma_0(N)\)-optimal |
| 7350.bo2 | 7350bu2 | \([1, 1, 1, -28813, -1843969]\) | \(1439069689/44100\) | \(81067514062500\) | \([2, 2]\) | \(36864\) | \(1.4447\) | |
| 7350.bo1 | 7350bu3 | \([1, 1, 1, -457563, -119321469]\) | \(5763259856089/5670\) | \(10422966093750\) | \([2]\) | \(73728\) | \(1.7913\) | |
| 7350.bo4 | 7350bu4 | \([1, 1, 1, 7937, -6180469]\) | \(30080231/9003750\) | \(-16551284121093750\) | \([2]\) | \(73728\) | \(1.7913\) |
Rank
sage: E.rank()
The elliptic curves in class 7350bu have rank \(1\).
Complex multiplication
The elliptic curves in class 7350bu do not have complex multiplication.Modular form 7350.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
