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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 2640.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2640.t1 | 2640v5 | \([0, 1, 0, -2737360, 1742282900]\) | \(553808571467029327441/12529687500\) | \(51321600000000\) | \([4]\) | \(36864\) | \(2.1549\) | |
| 2640.t2 | 2640v3 | \([0, 1, 0, -189200, -31669740]\) | \(182864522286982801/463015182960\) | \(1896510189404160\) | \([2]\) | \(18432\) | \(1.8083\) | |
| 2640.t3 | 2640v4 | \([0, 1, 0, -171280, 27115028]\) | \(135670761487282321/643043610000\) | \(2633906626560000\) | \([2, 4]\) | \(18432\) | \(1.8083\) | |
| 2640.t4 | 2640v6 | \([0, 1, 0, -83280, 55028628]\) | \(-15595206456730321/310672490129100\) | \(-1272514519568793600\) | \([4]\) | \(36864\) | \(2.1549\) | |
| 2640.t5 | 2640v2 | \([0, 1, 0, -16400, -81900]\) | \(119102750067601/68309049600\) | \(279793867161600\) | \([2, 2]\) | \(9216\) | \(1.4618\) | |
| 2640.t6 | 2640v1 | \([0, 1, 0, 4080, -8172]\) | \(1833318007919/1070530560\) | \(-4384893173760\) | \([2]\) | \(4608\) | \(1.1152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2640.t have rank \(0\).
Complex multiplication
The elliptic curves in class 2640.t do not have complex multiplication.Modular form 2640.2.a.t
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
