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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 44688cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44688.do3 | 44688cw1 | \([0, 1, 0, -126632, -10190412]\) | \(466025146777/177366672\) | \(85471279489548288\) | \([2]\) | \(368640\) | \(1.9483\) | \(\Gamma_0(N)\)-optimal |
| 44688.do2 | 44688cw2 | \([0, 1, 0, -894952, 318343220]\) | \(164503536215257/4178071044\) | \(2013371925526757376\) | \([2, 2]\) | \(737280\) | \(2.2948\) | |
| 44688.do4 | 44688cw3 | \([0, 1, 0, 147768, 1016965620]\) | \(740480746823/927484650666\) | \(-446945860264772542464\) | \([2]\) | \(1474560\) | \(2.6414\) | |
| 44688.do1 | 44688cw4 | \([0, 1, 0, -14230792, 20658166388]\) | \(661397832743623417/443352042\) | \(213647050298400768\) | \([2]\) | \(1474560\) | \(2.6414\) |
Rank
sage: E.rank()
The elliptic curves in class 44688cw have rank \(0\).
Complex multiplication
The elliptic curves in class 44688cw do not have complex multiplication.Modular form 44688.2.a.cw
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 Cremona 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 Cremona labels.
