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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 167310bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
167310.dy2 | 167310bq1 | \([1, -1, 1, -2777378, 1806363537]\) | \(-673350049820449/10617750000\) | \(-37361141568357750000\) | \([2]\) | \(6193152\) | \(2.5570\) | \(\Gamma_0(N)\)-optimal |
167310.dy1 | 167310bq2 | \([1, -1, 1, -44604878, 114673689537]\) | \(2789222297765780449/677605500\) | \(2384320125544285500\) | \([2]\) | \(12386304\) | \(2.9035\) |
Rank
sage: E.rank()
The elliptic curves in class 167310bq have rank \(1\).
Complex multiplication
The elliptic curves in class 167310bq do not have complex multiplication.Modular form 167310.2.a.bq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.