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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 11154q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11154.u3 | 11154q1 | \([1, 0, 1, -7609, 185564]\) | \(10091699281/2737152\) | \(13211709907968\) | \([2]\) | \(43200\) | \(1.2256\) | \(\Gamma_0(N)\)-optimal |
| 11154.u4 | 11154q2 | \([1, 0, 1, 19431, 1213084]\) | \(168105213359/228637728\) | \(-1103590643249952\) | \([2]\) | \(86400\) | \(1.5722\) | |
| 11154.u1 | 11154q3 | \([1, 0, 1, -1700989, -854028316]\) | \(112763292123580561/1932612\) | \(9328348995108\) | \([2]\) | \(216000\) | \(2.0303\) | |
| 11154.u2 | 11154q4 | \([1, 0, 1, -1699299, -855809576]\) | \(-112427521449300721/466873642818\) | \(-2253509901016707762\) | \([2]\) | \(432000\) | \(2.3769\) |
Rank
sage: E.rank()
The elliptic curves in class 11154q have rank \(0\).
Complex multiplication
The elliptic curves in class 11154q do not have complex multiplication.Modular form 11154.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
