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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 439569.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.u1 | 439569u2 | \([1, -1, 1, -144410, 14644140]\) | \(8615125/2601\) | \(100552174221170997\) | \([2]\) | \(3538944\) | \(1.9676\) | \(\Gamma_0(N)\)-optimal* |
439569.u2 | 439569u1 | \([1, -1, 1, 24655, 1524696]\) | \(42875/51\) | \(-1971611259238647\) | \([2]\) | \(1769472\) | \(1.6210\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.u have rank \(1\).
Complex multiplication
The elliptic curves in class 439569.u do not have complex multiplication.Modular form 439569.2.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.