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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 98736.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.ci1 | 98736dp1 | \([0, 1, 0, -4880, 81684]\) | \(1771561/612\) | \(4440864079872\) | \([2]\) | \(276480\) | \(1.1286\) | \(\Gamma_0(N)\)-optimal |
98736.ci2 | 98736dp2 | \([0, 1, 0, 14480, 585044]\) | \(46268279/46818\) | \(-339726102110208\) | \([2]\) | \(552960\) | \(1.4751\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.ci do not have complex multiplication.Modular form 98736.2.a.ci
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.