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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 259920gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.gb2 | 259920gb1 | \([0, 0, 0, -210387, 51360914]\) | \(-50284268371/26542080\) | \(-543604737551892480\) | \([2]\) | \(1966080\) | \(2.1073\) | \(\Gamma_0(N)\)-optimal |
| 259920.gb1 | 259920gb2 | \([0, 0, 0, -3712467, 2752865426]\) | \(276288773643091/41990400\) | \(859999682455142400\) | \([2]\) | \(3932160\) | \(2.4538\) |
Rank
sage: E.rank()
The elliptic curves in class 259920gb have rank \(0\).
Complex multiplication
The elliptic curves in class 259920gb do not have complex multiplication.Modular form 259920.2.a.gb
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.
