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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 212160.gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.gl1 | 212160ek1 | \([0, 1, 0, -1425, -21105]\) | \(19545784144/89505\) | \(1466449920\) | \([2]\) | \(114688\) | \(0.60971\) | \(\Gamma_0(N)\)-optimal |
| 212160.gl2 | 212160ek2 | \([0, 1, 0, -705, -41697]\) | \(-592143556/10989225\) | \(-720189849600\) | \([2]\) | \(229376\) | \(0.95628\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.gl have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.gl do not have complex multiplication.Modular form 212160.2.a.gl
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.
