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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 206910.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206910.y1 | 206910fd2 | \([1, -1, 0, -434715, 61389125]\) | \(260549802603/104256800\) | \(3635396579261858400\) | \([2]\) | \(5376000\) | \(2.2596\) | |
206910.y2 | 206910fd1 | \([1, -1, 0, 88005, 6921701]\) | \(2161700757/1848320\) | \(-64450244064476160\) | \([2]\) | \(2688000\) | \(1.9130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206910.y have rank \(0\).
Complex multiplication
The elliptic curves in class 206910.y do not have complex multiplication.Modular form 206910.2.a.y
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.