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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 221067.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.l1 | 221067g3 | \([1, -1, 1, -58104344, 170470952776]\) | \(16798320881842096017/2132227789307\) | \(2753703892501671207483\) | \([2]\) | \(20643840\) | \(3.1358\) | |
| 221067.l2 | 221067g4 | \([1, -1, 1, -23049434, -40847245172]\) | \(1048626554636928177/48569076788309\) | \(62725406956002467174421\) | \([2]\) | \(20643840\) | \(3.1358\) | |
| 221067.l3 | 221067g2 | \([1, -1, 1, -3942929, 2180604088]\) | \(5249244962308257/1448621666569\) | \(1870848481573261628361\) | \([2, 2]\) | \(10321920\) | \(2.7892\) | |
| 221067.l4 | 221067g1 | \([1, -1, 1, 636316, 222518926]\) | \(22062729659823/29354283343\) | \(-37910116690434740367\) | \([2]\) | \(5160960\) | \(2.4426\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221067.l have rank \(1\).
Complex multiplication
The elliptic curves in class 221067.l do not have complex multiplication.Modular form 221067.2.a.l
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.
