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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1290.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1290.b1 | 1290b1 | \([1, 1, 0, -154527, -23386059]\) | \(408076159454905367161/1190206406250000\) | \(1190206406250000\) | \([2]\) | \(10560\) | \(1.7632\) | \(\Gamma_0(N)\)-optimal |
| 1290.b2 | 1290b2 | \([1, 1, 0, -92027, -42398559]\) | \(-86193969101536367161/725294740213012500\) | \(-725294740213012500\) | \([2]\) | \(21120\) | \(2.1098\) |
Rank
sage: E.rank()
The elliptic curves in class 1290.b have rank \(0\).
Complex multiplication
The elliptic curves in class 1290.b do not have complex multiplication.Modular form 1290.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
