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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 106134bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106134.ch2 | 106134bq1 | \([1, 1, 1, 8476, 371909]\) | \(596183/864\) | \(-97594986482784\) | \([]\) | \(414720\) | \(1.3698\) | \(\Gamma_0(N)\)-optimal |
106134.ch1 | 106134bq2 | \([1, 1, 1, -256859, 50254889]\) | \(-16591834777/98304\) | \(-11104140684263424\) | \([]\) | \(1244160\) | \(1.9191\) |
Rank
sage: E.rank()
The elliptic curves in class 106134bq have rank \(1\).
Complex multiplication
The elliptic curves in class 106134bq do not have complex multiplication.Modular form 106134.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.