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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 162450ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162450.bs2 | 162450ey1 | \([1, -1, 0, 729333, -165843259]\) | \(2161700757/1848320\) | \(-36684496168560000000\) | \([2]\) | \(5529600\) | \(2.4417\) | \(\Gamma_0(N)\)-optimal |
162450.bs1 | 162450ey2 | \([1, -1, 0, -3602667, -1461111259]\) | \(260549802603/104256800\) | \(2069234862007837500000\) | \([2]\) | \(11059200\) | \(2.7882\) |
Rank
sage: E.rank()
The elliptic curves in class 162450ey have rank \(0\).
Complex multiplication
The elliptic curves in class 162450ey do not have complex multiplication.Modular form 162450.2.a.ey
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.