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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 324870.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 324870.bo1 | 324870bo3 | \([1, 0, 1, -362479, 83441852]\) | \(44769506062996441/323730468750\) | \(38086565917968750\) | \([2]\) | \(6193152\) | \(2.0132\) | |
| 324870.bo2 | 324870bo2 | \([1, 0, 1, -37609, -634504]\) | \(50002789171321/27473062500\) | \(3232178330062500\) | \([2, 2]\) | \(3096576\) | \(1.6666\) | |
| 324870.bo3 | 324870bo1 | \([1, 0, 1, -28789, -1879888]\) | \(22428153804601/35802000\) | \(4212069498000\) | \([2]\) | \(1548288\) | \(1.3201\) | \(\Gamma_0(N)\)-optimal |
| 324870.bo4 | 324870bo4 | \([1, 0, 1, 146141, -4971004]\) | \(2933972022568679/1789082460750\) | \(-210483762424776750\) | \([2]\) | \(6193152\) | \(2.0132\) |
Rank
sage: E.rank()
The elliptic curves in class 324870.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 324870.bo do not have complex multiplication.Modular form 324870.2.a.bo
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.
