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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9126.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9126.u1 | 9126bj3 | \([1, -1, 1, -20819, -1527821]\) | \(-1167051/512\) | \(-437788023768576\) | \([]\) | \(38880\) | \(1.5166\) | |
9126.u2 | 9126bj1 | \([1, -1, 1, -539, 5009]\) | \(-132651/2\) | \(-260647686\) | \([]\) | \(4320\) | \(0.41796\) | \(\Gamma_0(N)\)-optimal |
9126.u3 | 9126bj2 | \([1, -1, 1, 1996, 23599]\) | \(9261/8\) | \(-760048652376\) | \([]\) | \(12960\) | \(0.96727\) |
Rank
sage: E.rank()
The elliptic curves in class 9126.u have rank \(1\).
Complex multiplication
The elliptic curves in class 9126.u do not have complex multiplication.Modular form 9126.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.