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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 273600dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.dy4 | 273600dy1 | \([0, 0, 0, 134423700, -1275542062000]\) | \(89962967236397039/287450726400000\) | \(-858323269818777600000000000\) | \([2]\) | \(88473600\) | \(3.8513\) | \(\Gamma_0(N)\)-optimal |
| 273600.dy3 | 273600dy2 | \([0, 0, 0, -1266408300, -14944860718000]\) | \(75224183150104868881/11219310000000000\) | \(33500680151040000000000000000\) | \([2]\) | \(176947200\) | \(4.1979\) | |
| 273600.dy2 | 273600dy3 | \([0, 0, 0, -47541096300, -3989808404782000]\) | \(-3979640234041473454886161/1471455901872240\) | \(-4393743779696078684160000000\) | \([2]\) | \(442368000\) | \(4.6560\) | |
| 273600.dy1 | 273600dy4 | \([0, 0, 0, -760657608300, -255347690321518000]\) | \(16300610738133468173382620881/2228489100\) | \(6654232796774400000000\) | \([2]\) | \(884736000\) | \(5.0026\) |
Rank
sage: E.rank()
The elliptic curves in class 273600dy have rank \(1\).
Complex multiplication
The elliptic curves in class 273600dy do not have complex multiplication.Modular form 273600.2.a.dy
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.
