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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 430950.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.o1 | 430950o2 | \([1, 1, 0, -1185200, 495925500]\) | \(2441288319625/1217268\) | \(91805002153312500\) | \([2]\) | \(6193152\) | \(2.2077\) | \(\Gamma_0(N)\)-optimal* |
430950.o2 | 430950o1 | \([1, 1, 0, -86700, 4896000]\) | \(955671625/413712\) | \(31201700078250000\) | \([2]\) | \(3096576\) | \(1.8612\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.o have rank \(1\).
Complex multiplication
The elliptic curves in class 430950.o do not have complex multiplication.Modular form 430950.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.