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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 487872.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.cy1 | 487872cy2 | \([0, 0, 0, -1469424, 685579466]\) | \(35084566528/1029\) | \(10291160662542144\) | \([]\) | \(7299072\) | \(2.1723\) | \(\Gamma_0(N)\)-optimal* |
487872.cy2 | 487872cy1 | \([0, 0, 0, -31944, -673486]\) | \(360448/189\) | \(1890213182915904\) | \([]\) | \(2433024\) | \(1.6230\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 487872.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 487872.cy do not have complex multiplication.Modular form 487872.2.a.cy
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.