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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 35280bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.q3 | 35280bs1 | \([0, 0, 0, -31458, 2058343]\) | \(2508888064/118125\) | \(162097968690000\) | \([2]\) | \(147456\) | \(1.4874\) | \(\Gamma_0(N)\)-optimal |
| 35280.q2 | 35280bs2 | \([0, 0, 0, -86583, -7125482]\) | \(3269383504/893025\) | \(19607370292742400\) | \([2, 2]\) | \(294912\) | \(1.8340\) | |
| 35280.q4 | 35280bs3 | \([0, 0, 0, 222117, -46453862]\) | \(13799183324/18600435\) | \(-1633574050675338240\) | \([2]\) | \(589824\) | \(2.1805\) | |
| 35280.q1 | 35280bs4 | \([0, 0, 0, -1277283, -555561902]\) | \(2624033547076/324135\) | \(28466996869463040\) | \([2]\) | \(589824\) | \(2.1805\) |
Rank
sage: E.rank()
The elliptic curves in class 35280bs have rank \(1\).
Complex multiplication
The elliptic curves in class 35280bs do not have complex multiplication.Modular form 35280.2.a.bs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
