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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 140679.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140679.n1 | 140679j4 | \([1, -1, 1, -551039, -157201432]\) | \(215751695207833/163381911\) | \(14012632748037231\) | \([2]\) | \(1277952\) | \(2.0309\) | |
| 140679.n2 | 140679j2 | \([1, -1, 1, -41684, -1338802]\) | \(93391282153/44876601\) | \(3848891991434721\) | \([2, 2]\) | \(638976\) | \(1.6843\) | |
| 140679.n3 | 140679j1 | \([1, -1, 1, -21839, 1233110]\) | \(13430356633/180873\) | \(15512775603633\) | \([2]\) | \(319488\) | \(1.3377\) | \(\Gamma_0(N)\)-optimal |
| 140679.n4 | 140679j3 | \([1, -1, 1, 150151, -10316680]\) | \(4365111505607/3058314567\) | \(-262299777209384607\) | \([2]\) | \(1277952\) | \(2.0309\) |
Rank
sage: E.rank()
The elliptic curves in class 140679.n have rank \(0\).
Complex multiplication
The elliptic curves in class 140679.n do not have complex multiplication.Modular form 140679.2.a.n
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.
