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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 271040.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271040.cy1 | 271040cy3 | \([0, 0, 0, -161920748, 793052328112]\) | \(1010962818911303721/57392720\) | \(26653413719649812480\) | \([2]\) | \(23592960\) | \(3.1941\) | |
| 271040.cy2 | 271040cy4 | \([0, 0, 0, -16953068, -6336134992]\) | \(1160306142246441/634128110000\) | \(294491685828613898240000\) | \([2]\) | \(23592960\) | \(3.1941\) | |
| 271040.cy3 | 271040cy2 | \([0, 0, 0, -10138348, 12344375472]\) | \(248158561089321/1859334400\) | \(863482494058076569600\) | \([2, 2]\) | \(11796480\) | \(2.8475\) | |
| 271040.cy4 | 271040cy1 | \([0, 0, 0, -226028, 437696688]\) | \(-2749884201/176619520\) | \(-82022826893828423680\) | \([2]\) | \(5898240\) | \(2.5009\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271040.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 271040.cy do not have complex multiplication.Modular form 271040.2.a.cy
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.
