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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 355740.bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.bs1 | 355740bs4 | \([0, -1, 0, -294056660, 1023422250600]\) | \(52702650535889104/22020583921875\) | \(1174933123058368904076000000\) | \([2]\) | \(179159040\) | \(3.8913\) | |
| 355740.bs2 | 355740bs2 | \([0, -1, 0, -253502300, 1553618854152]\) | \(33766427105425744/9823275\) | \(524131931076805497600\) | \([2]\) | \(59719680\) | \(3.3420\) | |
| 355740.bs3 | 355740bs1 | \([0, -1, 0, -15779045, 24487788690]\) | \(-130287139815424/2250652635\) | \(-7505382063044470152240\) | \([2]\) | \(29859840\) | \(2.9954\) | \(\Gamma_0(N)\)-optimal |
| 355740.bs4 | 355740bs3 | \([0, -1, 0, 61060795, 117304552422]\) | \(7549996227362816/6152409907875\) | \(-20516798660519243588814000\) | \([2]\) | \(89579520\) | \(3.5448\) |
Rank
sage: E.rank()
The elliptic curves in class 355740.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 355740.bs do not have complex multiplication.Modular form 355740.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
