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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 164730.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164730.ci1 | 164730bd4 | \([1, 1, 1, -15265975611, -726003584520867]\) | \(16300610738133468173382620881/2228489100\) | \(53790309416997900\) | \([2]\) | \(122880000\) | \(4.0254\) | |
| 164730.ci2 | 164730bd3 | \([1, 1, 1, -954123391, -11344106285611]\) | \(-3979640234041473454886161/1471455901872240\) | \(-35517368361898422184560\) | \([2]\) | \(61440000\) | \(3.6789\) | |
| 164730.ci3 | 164730bd2 | \([1, 1, 1, -25416111, -42501389067]\) | \(75224183150104868881/11219310000000000\) | \(270806869257390000000000\) | \([2]\) | \(24576000\) | \(3.2207\) | |
| 164730.ci4 | 164730bd1 | \([1, 1, 1, 2697809, -3625460491]\) | \(89962967236397039/287450726400000\) | \(-6938361742580121600000\) | \([2]\) | \(12288000\) | \(2.8741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 164730.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 164730.ci do not have complex multiplication.Modular form 164730.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
