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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 283920.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.y1 | 283920y4 | \([0, -1, 0, -1135736, -465491040]\) | \(32779037733124/315\) | \(1556935511040\) | \([2]\) | \(2359296\) | \(1.9178\) | |
| 283920.y2 | 283920y5 | \([0, -1, 0, -1095176, 440010960]\) | \(14695548366242/57421875\) | \(567632738400000000\) | \([2]\) | \(4718592\) | \(2.2644\) | |
| 283920.y3 | 283920y3 | \([0, -1, 0, -101456, -405744]\) | \(23366901604/13505625\) | \(66753610035840000\) | \([2, 2]\) | \(2359296\) | \(1.9178\) | |
| 283920.y4 | 283920y2 | \([0, -1, 0, -71036, -7244160]\) | \(32082281296/99225\) | \(122608671494400\) | \([2, 2]\) | \(1179648\) | \(1.5712\) | |
| 283920.y5 | 283920y1 | \([0, -1, 0, -2591, -208014]\) | \(-24918016/229635\) | \(-17734468555440\) | \([2]\) | \(589824\) | \(1.2247\) | \(\Gamma_0(N)\)-optimal |
| 283920.y6 | 283920y6 | \([0, -1, 0, 405544, -3650544]\) | \(746185003198/432360075\) | \(-4274011138561382400\) | \([2]\) | \(4718592\) | \(2.2644\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.y have rank \(1\).
Complex multiplication
The elliptic curves in class 283920.y do not have complex multiplication.Modular form 283920.2.a.y
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
