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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 361920.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.cj1 | 361920cj4 | \([0, -1, 0, -4142145, -3243030975]\) | \(29981943972267024529/4007065140000\) | \(1050428084060160000\) | \([2]\) | \(7372800\) | \(2.4771\) | |
| 361920.cj2 | 361920cj3 | \([0, -1, 0, -1664065, 794097217]\) | \(1943993954077461649/87266819409120\) | \(22876473107184353280\) | \([4]\) | \(7372800\) | \(2.4771\) | |
| 361920.cj3 | 361920cj2 | \([0, -1, 0, -281665, -41148863]\) | \(9427227449071249/2652468249600\) | \(695328636823142400\) | \([2, 2]\) | \(3686400\) | \(2.1306\) | |
| 361920.cj4 | 361920cj1 | \([0, -1, 0, 46015, -4252095]\) | \(41102915774831/53367275520\) | \(-13989911073914880\) | \([2]\) | \(1843200\) | \(1.7840\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361920.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 361920.cj do not have complex multiplication.Modular form 361920.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
