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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 286650gl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.gl2 | 286650gl1 | \([1, -1, 0, -156688632, -827014195904]\) | \(-198417696411528597145/22989483914821632\) | \(-49292971479153644588236800\) | \([]\) | \(88704000\) | \(3.6663\) | \(\Gamma_0(N)\)-optimal |
286650.gl1 | 286650gl2 | \([1, -1, 0, -100506661992, -12264207734193584]\) | \(-134057911417971280740025/1872\) | \(-1567911899531250000\) | \([]\) | \(443520000\) | \(4.4710\) |
Rank
sage: E.rank()
The elliptic curves in class 286650gl have rank \(1\).
Complex multiplication
The elliptic curves in class 286650gl do not have complex multiplication.Modular form 286650.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.