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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 184041.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 184041.bq1 | 184041bp2 | \([1, -1, 0, -2396367, 1074605494]\) | \(244140625/61347\) | \(382416905392781560587\) | \([2]\) | \(5160960\) | \(2.6594\) | |
| 184041.bq2 | 184041bp1 | \([1, -1, 0, 364248, 106733875]\) | \(857375/1287\) | \(-8022732280967445327\) | \([2]\) | \(2580480\) | \(2.3128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 184041.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 184041.bq do not have complex multiplication.Modular form 184041.2.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.
