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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 301530cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301530.cy4 | 301530cy1 | \([1, 0, 0, 4938204, 8981615376]\) | \(89962967236397039/287450726400000\) | \(-42553023826319769600000\) | \([2]\) | \(29568000\) | \(3.0253\) | \(\Gamma_0(N)\)-optimal |
| 301530.cy3 | 301530cy2 | \([1, 0, 0, -46522916, 105224202000]\) | \(75224183150104868881/11219310000000000\) | \(1660860529816590000000000\) | \([2]\) | \(59136000\) | \(3.3719\) | |
| 301530.cy2 | 301530cy3 | \([1, 0, 0, -1746474996, 28092446393856]\) | \(-3979640234041473454886161/1471455901872240\) | \(-217828282557953812821360\) | \([2]\) | \(147840000\) | \(3.8300\) | |
| 301530.cy1 | 301530cy4 | \([1, 0, 0, -27943602416, 1797923220059700]\) | \(16300610738133468173382620881/2228489100\) | \(329896365045309900\) | \([2]\) | \(295680000\) | \(4.1766\) |
Rank
sage: E.rank()
The elliptic curves in class 301530cy have rank \(1\).
Complex multiplication
The elliptic curves in class 301530cy do not have complex multiplication.Modular form 301530.2.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 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.
