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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 214774o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214774.i2 | 214774o1 | \([1, 1, 0, -1123871, 725985029]\) | \(-1060490285861833/926330847232\) | \(-137130210478112309248\) | \([2]\) | \(8110080\) | \(2.5612\) | \(\Gamma_0(N)\)-optimal |
214774.i1 | 214774o2 | \([1, 1, 0, -20760351, 36389760005]\) | \(6684374974140996553/2097096248576\) | \(310445507476513144064\) | \([2]\) | \(16220160\) | \(2.9078\) |
Rank
sage: E.rank()
The elliptic curves in class 214774o have rank \(0\).
Complex multiplication
The elliptic curves in class 214774o do not have complex multiplication.Modular form 214774.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.