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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 98736.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.u1 | 98736t1 | \([0, -1, 0, -22304, -1273776]\) | \(676449508/561\) | \(1017698018304\) | \([2]\) | \(215040\) | \(1.2323\) | \(\Gamma_0(N)\)-optimal |
98736.u2 | 98736t2 | \([0, -1, 0, -17464, -1846832]\) | \(-162365474/314721\) | \(-1141857176537088\) | \([2]\) | \(430080\) | \(1.5789\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.u have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.u do not have complex multiplication.Modular form 98736.2.a.u
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.