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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 209484.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209484.bq1 | 209484be2 | \([0, 0, 0, -58719, -2603738]\) | \(810448/363\) | \(10028619058791168\) | \([2]\) | \(1216512\) | \(1.7658\) | |
209484.bq2 | 209484be1 | \([0, 0, 0, 12696, -304175]\) | \(131072/99\) | \(-170942370320304\) | \([2]\) | \(608256\) | \(1.4192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 209484.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 209484.bq do not have complex multiplication.Modular form 209484.2.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.