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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 17600.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17600.cy1 | 17600bu2 | \([0, -1, 0, -417033, -103519063]\) | \(125330290485184/378125\) | \(24200000000000\) | \([2]\) | \(92160\) | \(1.7958\) | |
17600.cy2 | 17600bu1 | \([0, -1, 0, -26408, -1565938]\) | \(2036792051776/107421875\) | \(107421875000000\) | \([2]\) | \(46080\) | \(1.4493\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17600.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 17600.cy do not have complex multiplication.Modular form 17600.2.a.cy
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.