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SageMath
E = EllipticCurve("oj1")
E.isogeny_class()
Elliptic curves in class 273600.oj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.oj1 | 273600oj3 | \([0, 0, 0, -13932300, 20012182000]\) | \(100162392144121/23457780\) | \(70044555755520000000\) | \([2]\) | \(18874368\) | \(2.7984\) | |
273600.oj2 | 273600oj4 | \([0, 0, 0, -6444300, -6123242000]\) | \(9912050027641/311647500\) | \(930574448640000000000\) | \([2]\) | \(18874368\) | \(2.7984\) | |
273600.oj3 | 273600oj2 | \([0, 0, 0, -972300, 235222000]\) | \(34043726521/11696400\) | \(34925263257600000000\) | \([2, 2]\) | \(9437184\) | \(2.4519\) | |
273600.oj4 | 273600oj1 | \([0, 0, 0, 179700, 25558000]\) | \(214921799/218880\) | \(-653572177920000000\) | \([2]\) | \(4718592\) | \(2.1053\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 273600.oj have rank \(1\).
Complex multiplication
The elliptic curves in class 273600.oj do not have complex multiplication.Modular form 273600.2.a.oj
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.