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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 140790cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.a3 | 140790cq1 | \([1, 1, 0, -2702453, -1712610003]\) | \(-46395601158168289/47939973120\) | \(-2255378270546718720\) | \([2]\) | \(4976640\) | \(2.4396\) | \(\Gamma_0(N)\)-optimal |
140790.a2 | 140790cq2 | \([1, 1, 0, -43249973, -109496027667]\) | \(190177723376764332769/202737600\) | \(9537969003825600\) | \([2]\) | \(9953280\) | \(2.7862\) | |
140790.a4 | 140790cq3 | \([1, 1, 0, 3275707, -7724611587]\) | \(82626060291589151/595927492758000\) | \(-28035933908921229798000\) | \([2]\) | \(14929920\) | \(2.9889\) | |
140790.a1 | 140790cq4 | \([1, 1, 0, -44311313, -103840874583]\) | \(204524800857359188129/19379962604437500\) | \(911747414472816696937500\) | \([2]\) | \(29859840\) | \(3.3355\) |
Rank
sage: E.rank()
The elliptic curves in class 140790cq have rank \(0\).
Complex multiplication
The elliptic curves in class 140790cq do not have complex multiplication.Modular form 140790.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.