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SageMath
E = EllipticCurve("nq1")
E.isogeny_class()
Elliptic curves in class 221760.nq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.nq1 | 221760mn1 | \([0, 0, 0, -12053772, -16105617936]\) | \(37537160298467283/5519360000\) | \(28478685283614720000\) | \([2]\) | \(8257536\) | \(2.7472\) | \(\Gamma_0(N)\)-optimal |
| 221760.nq2 | 221760mn2 | \([0, 0, 0, -10947852, -19180517904]\) | \(-28124139978713043/14526050000000\) | \(-74951227382169600000000\) | \([2]\) | \(16515072\) | \(3.0938\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.nq have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.nq do not have complex multiplication.Modular form 221760.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
