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SageMath
sage: E = EllipticCurve("q1")
sage: E.isogeny_class()
Elliptic curves in class 221067.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
221067.q1 | 221067q1 | [0, 0, 1, -68970, 10505250] | [] | 1209600 | \(\Gamma_0(N)\)-optimal |
221067.q2 | 221067q2 | [0, 0, 1, 562650, -162148077] | [] | 3628800 |
Rank
sage: E.rank()
The elliptic curves in class 221067.q have rank \(0\).
Complex multiplication
The elliptic curves in class 221067.q do not have complex multiplication.Modular form 221067.2.a.q
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.