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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 5610.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5610.bi1 | 5610bg3 | \([1, 0, 0, -107371, 4812815]\) | \(136894171818794254129/69177425857031250\) | \(69177425857031250\) | \([2]\) | \(81920\) | \(1.9239\) | |
| 5610.bi2 | 5610bg2 | \([1, 0, 0, -86801, 9827781]\) | \(72326626749631816849/69403061722500\) | \(69403061722500\) | \([2, 2]\) | \(40960\) | \(1.5773\) | |
| 5610.bi3 | 5610bg1 | \([1, 0, 0, -86781, 9832545]\) | \(72276643492008825169/66646800\) | \(66646800\) | \([4]\) | \(20480\) | \(1.2307\) | \(\Gamma_0(N)\)-optimal |
| 5610.bi4 | 5610bg4 | \([1, 0, 0, -66551, 14537931]\) | \(-32597768919523300849/72509045805004050\) | \(-72509045805004050\) | \([2]\) | \(81920\) | \(1.9239\) |
Rank
sage: E.rank()
The elliptic curves in class 5610.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 5610.bi do not have complex multiplication.Modular form 5610.2.a.bi
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.
