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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 239343.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
239343.d1 | 239343d2 | \([1, 0, 0, -808106, 159900693]\) | \(1240529607439849/482920342983\) | \(22719412988457403023\) | \([2]\) | \(6912000\) | \(2.4129\) | |
239343.d2 | 239343d1 | \([1, 0, 0, -362271, -82187712]\) | \(111764245610809/2697634953\) | \(126912612980278593\) | \([2]\) | \(3456000\) | \(2.0664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 239343.d have rank \(0\).
Complex multiplication
The elliptic curves in class 239343.d do not have complex multiplication.Modular form 239343.2.a.d
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.