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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 135240bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135240.i2 | 135240bu1 | \([0, -1, 0, -217576, 39078460]\) | \(27566165308/46575\) | \(1924576507929600\) | \([2]\) | \(974848\) | \(1.8278\) | \(\Gamma_0(N)\)-optimal |
| 135240.i1 | 135240bu2 | \([0, -1, 0, -286176, 12434220]\) | \(31362635054/17353845\) | \(1434194413709137920\) | \([2]\) | \(1949696\) | \(2.1744\) |
Rank
sage: E.rank()
The elliptic curves in class 135240bu have rank \(0\).
Complex multiplication
The elliptic curves in class 135240bu do not have complex multiplication.Modular form 135240.2.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.
