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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 236992.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.cq1 | 236992cq2 | \([0, -1, 0, -796321, -118232127]\) | \(5756278756/2705927\) | \(26252037915548254208\) | \([2]\) | \(8110080\) | \(2.4205\) | |
236992.cq2 | 236992cq1 | \([0, -1, 0, 177039, -14082607]\) | \(253012016/181447\) | \(-440085183715459072\) | \([2]\) | \(4055040\) | \(2.0739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.cq do not have complex multiplication.Modular form 236992.2.a.cq
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.