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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 129360.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.cj1 | 129360ff4 | \([0, -1, 0, -2344739000, 43543071296880]\) | \(2958414657792917260183849/12401051653985258880\) | \(5975946551458659213201899520\) | \([2]\) | \(115605504\) | \(4.1845\) | |
| 129360.cj2 | 129360ff2 | \([0, -1, 0, -219785400, -71176352400]\) | \(2436531580079063806249/1405478914998681600\) | \(677286661614304835823206400\) | \([2, 2]\) | \(57802752\) | \(3.8379\) | |
| 129360.cj3 | 129360ff1 | \([0, -1, 0, -155560120, -744873849488]\) | \(863913648706111516969/2486234429521920\) | \(1198092265057584603463680\) | \([2]\) | \(28901376\) | \(3.4913\) | \(\Gamma_0(N)\)-optimal |
| 129360.cj4 | 129360ff3 | \([0, -1, 0, 877563720, -569811792528]\) | \(155099895405729262880471/90047655797243760000\) | \(-43393092226621157868503040000\) | \([2]\) | \(115605504\) | \(4.1845\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.cj do not have complex multiplication.Modular form 129360.2.a.cj
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.
