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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 69360.dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69360.dx1 | 69360bt4 | \([0, 1, 0, -62520, 5992308]\) | \(546718898/405\) | \(20020665231360\) | \([2]\) | \(327680\) | \(1.4860\) | |
| 69360.dx2 | 69360bt3 | \([0, 1, 0, -39400, -2987500]\) | \(136835858/1875\) | \(92688264960000\) | \([2]\) | \(327680\) | \(1.4860\) | |
| 69360.dx3 | 69360bt2 | \([0, 1, 0, -4720, 50468]\) | \(470596/225\) | \(5561295897600\) | \([2, 2]\) | \(163840\) | \(1.1394\) | |
| 69360.dx4 | 69360bt1 | \([0, 1, 0, 1060, 6540]\) | \(21296/15\) | \(-92688264960\) | \([2]\) | \(81920\) | \(0.79286\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69360.dx have rank \(1\).
Complex multiplication
The elliptic curves in class 69360.dx do not have complex multiplication.Modular form 69360.2.a.dx
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
