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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 209814.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209814.cq1 | 209814bk2 | \([1, 1, 1, -5751960002, 167905800418511]\) | \(2418067440128989194388361/8359273562112\) | \(72756435371149207535616\) | \([2]\) | \(196116480\) | \(4.0306\) | |
209814.cq2 | 209814bk1 | \([1, 1, 1, -359657922, 2620957062351]\) | \(591139158854005457801/1097587482427392\) | \(9553049333300544883654656\) | \([2]\) | \(98058240\) | \(3.6840\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 209814.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 209814.cq do not have complex multiplication.Modular form 209814.2.a.cq
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.