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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 270504.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270504.ce1 | 270504ce1 | \([0, 0, 0, -1694118, -797355335]\) | \(1909913257984/129730653\) | \(36524446508794624848\) | \([2]\) | \(9830400\) | \(2.5023\) | \(\Gamma_0(N)\)-optimal |
270504.ce2 | 270504ce2 | \([0, 0, 0, 1466097, -3429814430]\) | \(77366117936/1172914587\) | \(-5283569315543821615872\) | \([2]\) | \(19660800\) | \(2.8489\) |
Rank
sage: E.rank()
The elliptic curves in class 270504.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 270504.ce do not have complex multiplication.Modular form 270504.2.a.ce
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.