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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 284592.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.bq1 | 284592bq4 | \([0, -1, 0, -2800464, -1802642400]\) | \(5690357426/891\) | \(380322489670244352\) | \([2]\) | \(5898240\) | \(2.3843\) | |
284592.bq2 | 284592bq2 | \([0, -1, 0, -191704, -22424576]\) | \(3650692/1089\) | \(232419299242927104\) | \([2, 2]\) | \(2949120\) | \(2.0377\) | |
284592.bq3 | 284592bq1 | \([0, -1, 0, -73124, 7362720]\) | \(810448/33\) | \(1760752266991872\) | \([2]\) | \(1474560\) | \(1.6912\) | \(\Gamma_0(N)\)-optimal |
284592.bq4 | 284592bq3 | \([0, -1, 0, 519776, -150490976]\) | \(36382894/43923\) | \(-18748490138929453056\) | \([2]\) | \(5898240\) | \(2.3843\) |
Rank
sage: E.rank()
The elliptic curves in class 284592.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 284592.bq do not have complex multiplication.Modular form 284592.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.