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SageMath
E = EllipticCurve("nq1")
E.isogeny_class()
Elliptic curves in class 277200.nq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.nq1 | 277200nq2 | \([0, 0, 0, -96445200, -6892234634000]\) | \(-2126464142970105856/438611057788643355\) | \(-20463837512186944370880000000\) | \([]\) | \(230400000\) | \(4.1117\) | |
277200.nq2 | 277200nq1 | \([0, 0, 0, -32185200, 82303846000]\) | \(-79028701534867456/16987307596875\) | \(-792559823239800000000000\) | \([]\) | \(46080000\) | \(3.3069\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.nq have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.nq do not have complex multiplication.Modular form 277200.2.a.nq
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.