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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 9450.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.cy1 | 9450ci1 | \([1, -1, 1, -32930, 2309697]\) | \(-14976927675/10976\) | \(-2894062500000\) | \([]\) | \(37800\) | \(1.3254\) | \(\Gamma_0(N)\)-optimal |
9450.cy2 | 9450ci2 | \([1, -1, 1, 32695, 9834697]\) | \(20108925/229376\) | \(-44089920000000000\) | \([]\) | \(113400\) | \(1.8747\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.cy do not have complex multiplication.Modular form 9450.2.a.cy
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.