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SageMath
sage: E = EllipticCurve("iq1")
sage: E.isogeny_class()
Elliptic curves in class 221760iq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 221760.lq6 | 221760iq1 | [0, 0, 0, 20148, 319761776] | [2] | 3932160 | \(\Gamma_0(N)\)-optimal |
| 221760.lq5 | 221760iq2 | [0, 0, 0, -6894732, 6844642544] | [2, 2] | 7864320 | |
| 221760.lq2 | 221760iq3 | [0, 0, 0, -109771212, 442670562416] | [2, 2] | 15728640 | |
| 221760.lq4 | 221760iq4 | [0, 0, 0, -14656332, -11388908176] | [2] | 15728640 | |
| 221760.lq1 | 221760iq5 | [0, 0, 0, -1756339212, 28330922092016] | [2] | 31457280 | |
| 221760.lq3 | 221760iq6 | [0, 0, 0, -109226892, 447277904624] | [2] | 31457280 |
Rank
sage: E.rank()
The elliptic curves in class 221760iq have rank \(0\).
Complex multiplication
The elliptic curves in class 221760iq do not have complex multiplication.Modular form 221760.2.a.iq
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
