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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 16758.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16758.bg1 | 16758bc3 | \([1, -1, 1, -37715, -22667277]\) | \(-69173457625/2550136832\) | \(-218715344099868672\) | \([]\) | \(204120\) | \(2.0074\) | |
| 16758.bg2 | 16758bc1 | \([1, -1, 1, -6845, 219741]\) | \(-413493625/152\) | \(-13036450392\) | \([]\) | \(22680\) | \(0.90882\) | \(\Gamma_0(N)\)-optimal |
| 16758.bg3 | 16758bc2 | \([1, -1, 1, 4180, 827439]\) | \(94196375/3511808\) | \(-301194149856768\) | \([]\) | \(68040\) | \(1.4581\) |
Rank
sage: E.rank()
The elliptic curves in class 16758.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 16758.bg do not have complex multiplication.Modular form 16758.2.a.bg
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
