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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 83790ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.bo4 | 83790ch1 | \([1, -1, 0, 4116726, -6837137420]\) | \(89962967236397039/287450726400000\) | \(-24653533781960294400000\) | \([2]\) | \(6912000\) | \(2.9798\) | \(\Gamma_0(N)\)-optimal |
| 83790.bo3 | 83790ch2 | \([1, -1, 0, -38783754, -80085416972]\) | \(75224183150104868881/11219310000000000\) | \(962236698996510000000000\) | \([2]\) | \(13824000\) | \(3.3264\) | |
| 83790.bo2 | 83790ch3 | \([1, -1, 0, -1455946074, -21382515432860]\) | \(-3979640234041473454886161/1471455901872240\) | \(-126201064926138662381040\) | \([2]\) | \(34560000\) | \(3.7845\) | |
| 83790.bo1 | 83790ch4 | \([1, -1, 0, -23295139254, -1368498204032072]\) | \(16300610738133468173382620881/2228489100\) | \(191128865797781100\) | \([2]\) | \(69120000\) | \(4.1311\) |
Rank
sage: E.rank()
The elliptic curves in class 83790ch have rank \(1\).
Complex multiplication
The elliptic curves in class 83790ch do not have complex multiplication.Modular form 83790.2.a.ch
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.
