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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 288990j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 288990.j2 | 288990j1 | \([1, -1, 0, -149850, -24459980]\) | \(-105756712489/12476160\) | \(-43900410161237760\) | \([2]\) | \(3612672\) | \(1.9292\) | \(\Gamma_0(N)\)-optimal |
| 288990.j1 | 288990j2 | \([1, -1, 0, -2461770, -1486055804]\) | \(468898230633769/5540400\) | \(19495247933444400\) | \([2]\) | \(7225344\) | \(2.2758\) |
Rank
sage: E.rank()
The elliptic curves in class 288990j have rank \(1\).
Complex multiplication
The elliptic curves in class 288990j do not have complex multiplication.Modular form 288990.2.a.j
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.
