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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 318402.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 318402.bu1 | 318402bu2 | \([1, -1, 0, -12060142404, -510564722565808]\) | \(-133179212896925841/240518168576\) | \(-350342209237947135125971009536\) | \([]\) | \(514805760\) | \(4.5612\) | |
| 318402.bu2 | 318402bu1 | \([1, -1, 0, 8885406, 297914186996]\) | \(53261199/26353376\) | \(-38386704935352543835002336\) | \([]\) | \(73543680\) | \(3.5882\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 318402.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 318402.bu do not have complex multiplication.Modular form 318402.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
