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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 4560.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.o1 | 4560s4 | \([0, -1, 0, -845175120, 9457603588800]\) | \(16300610738133468173382620881/2228489100\) | \(9127891353600\) | \([2]\) | \(576000\) | \(3.3020\) | |
| 4560.o2 | 4560s3 | \([0, -1, 0, -52823440, 147788289472]\) | \(-3979640234041473454886161/1471455901872240\) | \(-6027083374068695040\) | \([2]\) | \(288000\) | \(2.9554\) | |
| 4560.o3 | 4560s2 | \([0, -1, 0, -1407120, 553982400]\) | \(75224183150104868881/11219310000000000\) | \(45954293760000000000\) | \([2]\) | \(115200\) | \(2.4973\) | |
| 4560.o4 | 4560s1 | \([0, -1, 0, 149360, 47192512]\) | \(89962967236397039/287450726400000\) | \(-1177398175334400000\) | \([2]\) | \(57600\) | \(2.1507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.o have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.o do not have complex multiplication.Modular form 4560.2.a.o
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.
