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SageMath
sage: E = EllipticCurve("u1")
sage: E.isogeny_class()
Elliptic curves in class 29400u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
29400.b1 | 29400u1 | [0, -1, 0, -21408, 1210812] | [2] | 92160 | \(\Gamma_0(N)\)-optimal |
29400.b2 | 29400u2 | [0, -1, 0, -14408, 2008812] | [2] | 184320 |
Rank
sage: E.rank()
The elliptic curves in class 29400u have rank \(0\).
Complex multiplication
The elliptic curves in class 29400u do not have complex multiplication.Modular form 29400.2.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 Cremona 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 Cremona labels.