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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 15600.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bq1 | 15600cy2 | \([0, 1, 0, -145568, 19649268]\) | \(666276475992821/58199166792\) | \(29797973397504000\) | \([2]\) | \(147456\) | \(1.9017\) | |
| 15600.bq2 | 15600cy1 | \([0, 1, 0, -142368, 20628468]\) | \(623295446073461/5458752\) | \(2794881024000\) | \([2]\) | \(73728\) | \(1.5551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.bq do not have complex multiplication.Modular form 15600.2.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 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.
