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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 2640.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2640.u1 | 2640m3 | \([0, 1, 0, -52800, -4687452]\) | \(15897679904620804/2475\) | \(2534400\) | \([2]\) | \(4096\) | \(1.0754\) | |
| 2640.u2 | 2640m5 | \([0, 1, 0, -28000, 1759508]\) | \(1185450336504002/26043266205\) | \(53336609187840\) | \([4]\) | \(8192\) | \(1.4220\) | |
| 2640.u3 | 2640m4 | \([0, 1, 0, -3800, -50652]\) | \(5927735656804/2401490025\) | \(2459125785600\) | \([2, 4]\) | \(4096\) | \(1.0754\) | |
| 2640.u4 | 2640m2 | \([0, 1, 0, -3300, -74052]\) | \(15529488955216/6125625\) | \(1568160000\) | \([2, 2]\) | \(2048\) | \(0.72881\) | |
| 2640.u5 | 2640m1 | \([0, 1, 0, -175, -1552]\) | \(-37256083456/38671875\) | \(-618750000\) | \([2]\) | \(1024\) | \(0.38224\) | \(\Gamma_0(N)\)-optimal |
| 2640.u6 | 2640m6 | \([0, 1, 0, 12400, -355212]\) | \(102949393183198/86815346805\) | \(-177797830256640\) | \([4]\) | \(8192\) | \(1.4220\) |
Rank
sage: E.rank()
The elliptic curves in class 2640.u have rank \(0\).
Complex multiplication
The elliptic curves in class 2640.u do not have complex multiplication.Modular form 2640.2.a.u
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.
