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SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 221760.hy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.hy1 | 221760cy2 | \([0, 0, 0, -964452, -6892234634]\) | \(-2126464142970105856/438611057788643355\) | \(-20463837512186944370880\) | \([]\) | \(19200000\) | \(2.9604\) | |
221760.hy2 | 221760cy1 | \([0, 0, 0, -321852, 82303846]\) | \(-79028701534867456/16987307596875\) | \(-792559823239800000\) | \([]\) | \(3840000\) | \(2.1556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221760.hy have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.hy do not have complex multiplication.Modular form 221760.2.a.hy
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.