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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 106722.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.q1 | 106722bw2 | \([1, -1, 0, -774846, -263672172]\) | \(-16591834777/98304\) | \(-304822477806206976\) | \([]\) | \(1944000\) | \(2.1952\) | |
106722.q2 | 106722bw1 | \([1, -1, 0, 25569, -1936467]\) | \(596183/864\) | \(-2679103808843616\) | \([]\) | \(648000\) | \(1.6459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106722.q have rank \(1\).
Complex multiplication
The elliptic curves in class 106722.q do not have complex multiplication.Modular form 106722.2.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.