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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 48672.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48672.y1 | 48672m2 | \([0, 0, 0, -1997580, 1086056192]\) | \(61162984000/41067\) | \(591889408135114752\) | \([2]\) | \(860160\) | \(2.3486\) | |
48672.y2 | 48672m1 | \([0, 0, 0, -149565, 9772256]\) | \(1643032000/767637\) | \(172871545885616448\) | \([2]\) | \(430080\) | \(2.0020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48672.y have rank \(0\).
Complex multiplication
The elliptic curves in class 48672.y do not have complex multiplication.Modular form 48672.2.a.y
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.