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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 236992.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.cn1 | 236992cn2 | \([0, -1, 0, -5654657, 4899954977]\) | \(1030541881826/62236321\) | \(1207593744115219693568\) | \([2]\) | \(8110080\) | \(2.7977\) | |
236992.cn2 | 236992cn1 | \([0, -1, 0, -5570017, 5061634305]\) | \(1969910093092/7889\) | \(76536553689645056\) | \([2]\) | \(4055040\) | \(2.4511\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.cn do not have complex multiplication.Modular form 236992.2.a.cn
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.